A convention to improve definition, originally used when partner opens 1NT and the next player overcalls in a suit at the two-level.
The basis of the convention is the use of a bid of 2NT as a conventional request for opener to bid 3♣. This then creates an extra echelon of bids — direct bids, and bids after the Lebensohl 2NT.
One sequence shows game-going values (traditionally the direct bid) whilst the other is employed on competitive hands (or invitational hands if a competitive bid in the suit was available at the two-level). By agreement, a double may show a traditional penalty double or may show a raise to 2NT.
For example if your partner opens 1NT and the next hand overcalls 2♥:
2♠ – natural, competitive.
2NT – asks opener to bid 3♣; usually weak with a minor or invitational with spades.
3♣/3♦/3♠ – game-forcing.
On both hands, you bid 2NT over the intervening 2♥. On the first hand, you intend to convert 3♣ to 3♦, which will ask partner to pass. On the second, you intend to rebid 3♠ to invite game.
Responder may also use the convention on balanced hands to show or deny a stopper in the suit overcalled or to show or deny four cards in the other major. The most logical system (though perhaps not the most widely played) is:
3NT direct – stopper in suit overcalled and no interest in other major No stopper in suit or interest in other major.
Cue bid – no stopper but interest in other major
2NT and then 3NT – stopper and interest in other major.
2NT then cue bid – no stopper but interest in other major.
Many pairs who play Lebensohl also use it after the opponents open a weak two and partner doubles for take-out.
With the first hand, you have little interest in game and so bid 2NT, Lebensohl, on the way to 3♦. On the second you want to show positive values without going past 3NT. You do this by bidding 3♦ directly.