The basic principle behind the Lebensohl convention is to use a 2NT bid as an artificial relay, asking partner to bid 3♣️. This can be applied in numerous auctions. Lebensohl is most frequently applied, when partner’s 1NT opening is overcalled by RHO.

1NT - Double or 2♣️

1NT - 2 of a suit (natural) - 2NT - 3♣️

Unbalanced Hands

1NT-2❤️ Balanced Hands

1NT - 2♦️ Multi-Landy Type

RHO intervenes with a 2♦️, showing a one-suited overcall in an unspecified major.
You can still bid 2❤️ or 2♠️, natural and non-invitational. Any suit bid at the three-level, whether a jump or not, is natural and game-forcing.
If you want to compete in either minor, you start with the 2NT Lebensohl relay and either pass partner’s forced 3♣️ response or convert to 3♦️ (non-invitational). With a balanced hand and a four-card major, use Double as Stayman. Opener bids 2NT without a four-card major.

Artificial Overcalls: Both Majors Type

RHO will often overcall with a bid showing both majors, perhaps Two Clubs (Landy) or Two Diamonds (Cappelletti). After such a bid, the best strategy is probably to give up trying to find a major-suit fit. Even if you find a 4-4 fit, you know that trumps are going to break at best 4-1, and perhaps 5-0.

Sources:
25 Bridge Conventions You Should Know by Barbara Seagram, Marc Smith and David Bird
Lebensohl After a 1NT Opening Bid by Marc Smith
Series of articles by Vic Quiros published in Bridge Bulletin 12/23, 1/24, and 2/24

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