If you don't use Lebensohl you probably should.
Lebensohl is a useful convention which helps with competitive bidding when an opponent overcalls your partner’s 1NT opening. If the overcall is 2 clubs then you can bid 2 diamonds, hearts or spades to compete for the contract with a 5 card suit and as little as 6-9 points but what if the overcall is 2 spades? You now have to bid at the 3 level where a new suit is normally forcing.
With this hand, playing a weak no trump, you just want to play in 3C. You could agree with your partner that 3C is a weak bid here but what do you do then with the next hand?
With this hand, you want to show that you have a good suit and a strong hand without going past 3NT in case partner has a stop and 3NT is the best contract. You need 3C to be strong.
Lebensohl solves this problem by using 2NT as an artificial bid which is a relay to 3C. You can pass this with a club suit or correct it to a suit of your choice, to show a long suit in a weak hand. Partner will know you are weak since you bid Lebensohl 2NT before bidding 3 of your suit. If you have a strong hand, however, you can just bid 3 of your suit directly over the intervention to make a game force.
This is the basic idea of the Lebensohl 2NT bid. You can show both a weak hand and a strong hand without going past 3NT.
If the overcall is in a suit lower than yours, however, say 2D when you have hearts, you can simply bid 2H to show a weak hand with a 5+ heart suit. You can now use the Lebensohl 2NT to show an invitational hand with about 11-12 points and 7 losers. Partner should bid game with a fit and a working 13+ points.
This hand has 11 points, all working. After a 2D overcall I would bid 2NT and, over partner’s 3C, bid 3H to invite them to bid game with a suitable hand
Note that you do not force to game with the above hand despite the fact that it has only 7 losers. You do not yet know whether you have an 8+ card fit and a hand which opens 1NT often has 8 losers so even with a fit, game may not be possible.
If you are not a great fan of gadgets and complicated systems you could just stop here with what Bernard Magee calls Lebensohl Light - the use of 2NT to show weak or intermediate hands after an overcall of your partner's 1NT. I believe that all partnerships could benefit from the extra flexibility this gives with relatively little memory overhead. Jump to the bit at the end about the use of Lebensohl after the double of a weak two though. Lebensohl Light is useful there also.
The price that we pay, however, is that we lose 2NT as a natural invitational bid with a stop in the overcaller’s suit. If you want to play in no trumps then it must be at the 3 level but the full Lebensohl system recognises that if you do want to play in 3NT, you have two ways to bid it. You can bid 3N immediately, or, you can bid 2NT first and then bid 3NT over partner’s 3C. One way can be used to show that you have a stop in the overcaller’s suit while the other can deny a stop. When agreeing to play Lebensohl it is essential to check which way round these two sequences are played.
If someone says they play ‘slow shows’ then using Lebensohl 2NT before bidding 3NT shows a stop in the overcaller’s suit while an immediate 3NT denies a stop. Conversely, ‘fast shows’ means that an immediate 3NT shows a stop and going through Lebensohl 2NT before bidding 3NT denies a stop. I play ‘slow shows’ and the rest of this article assumes this convention.
After 1NT – (2S), you want to show a spade stop and values to play in 3NT so ‘slow shows’. You bid 2NT first and then, after partner’s 3C relay, 3NT to show a spade stop and no trump shape.
Here, after a 2S overcall, partner almost certainly has values in spades and the lead will be coming up to him. Bid 3NT immediately to deny a stop (or 4 cards in hearts. See later).
You are very close to having the values for an immediate 3D bid but this is best kept for a game forcing hand with slam possibilities. If you were 3:1 and not 2:2 in the black suits you might consider 3D but even then I think that 3NT is the practical bid. You might think that this is a little dangerous. What if partner has no stop? Well, in most cases they will have a stop. If not, they will bid their best suit and with this hand you can pass over 4H or bid 5 diamonds over 4C. Note that if partner has no stop then their values are in clubs and hearts.
You may be thinking "Why don’t you just bid 3S to ask partner for a stop?" The answer is because Lebensohl uses a bid of the overcaller’s suit as a game forcing Stayman-like bid to show a 4 card major. If the overcall is in a natural minor suit then it shows at least one 4 card major. If the overcall is in a major suit, or an artificial bid which shows a major suit, then your cue-bid shows 4 cards in the other major. Again, it can be bid immediately, showing no stop in the bid suit, or, after 2NT to show a stop.
After 1NT – (2H) bid 3H immediately to show a 4 card spade suit with game values but no stop in hearts. Swap the diamond and heart holdings and you bid 2NT first then 3H over partner’s 3C to show 4 cards in spades with a stop in hearts.
This full version of Lebensohl lets you distinguish between game going hands with or without stops and with or without 4 card majors by using cue bids, 2NT and 3NT appropriately. It is, however, extremely easy to get it wrong at the table and is only for established partnerships who are willing to put in the time to master it.
Summary of Lebensohl Bids after Partner's 1NT is overcalled with 2X
A 2 level response (if possible) is competitive but non forcing
A 3 level response in a new suit is always game forcing showing 5+ cards in the bid suit
A cuebid of the opponent's suit (including a suit promised by an artificial bid) is game forcing showing a 4 card major but no stopper in the opposition's suit.
3NT is to play but with no stopper in opponent's suit, nor a 4 card major.
2NT (Lebensohl) is a relay to 3C. Your rebids are now:
pass - competitive with a club suit but non-forcing
3 of a new suit - competitive if the suit could not have been bid at the two level or an invitation to game if the suit could have been bid at the 2 level
3 of the opponent's suit - a game force showing the other or at least one 4 card major with a stopper in the opponent's suit.
3NT - a natural bid with a stopper in the opponent's suit (slow shows) and no 4 card major.
Use of Lebensohl after a double of a weak two bid
A similar bidding structure can be used after partner's double of a weak 2 bid. You have the same problem in that you have lost space in the bidding and need a method to show both weak and stronger hands without going past 3NT. The key difference is that passing is not an option with a weak hand! This means that when your suit is lower than the overcaller's suit you use Lebensohl to show a weak hand (< 8 points) and the immediate 3 bid to show an invitational hand (8-11) not a game forcing one since you can bid game directly to show the stronger hand.
As before, you can just use the Lebensohl Light version if you prefer.
Summary
A 2 level response (if possible) is weak (<8)
A non-jump 3 level response in a new suit is now invitational (~8-11)
A jump 3 level response in a new suit is still game forcing
A cuebid of the opponent's suit (including a suit promised by an artificial bid) is game forcing showing a 4 card major but no stopper in the opposition's suit.
3NT is to play but with no stopper in opponent's suit, nor a 4 card major.
2NT (Lebensohl) is a relay to 3C. Your rebids are:
pass - with a club suit and <8
3 of a new suit - weak if the suit could not have been bid at the two level or an invitation to game if the suit could have been bid at the 2 level
3 of the opponent's suit - a game force showing the other or at least one 4 card major with a stopper in the opponent's suit.
3NT - a natural bid with a stopper in the opponent's suit (slow shows) and no 4 card major.