Lebensohl
A Lebensohl response usually refers to responding to a takeout double of a weak-2 bid.
Responder bids 2NT, not as a natural bid, but to force partner to bid 3C. Responder can now make a further descriptive bid. It allows responder to signoff in 3-of-a-lower suit (by relaying then bidding the suit), to invite (by relaying then bidding a higher suit), to force (by jumping), to show values for no-trump combined with either showing or denying a stopper in the weak-2 suit, etc.
There are many variations. One can play a similar system after opponents make an overcall over your partner's 1NT opening bid.
2NT response to a double of 2 of a major asks partner to bid better minor.
Doubler's bid of anything else shows a strong hand with suit bid.
Re-bids by 2NT bidder:
BID Directly After bidding 2NT
3C To Play 3 of lower suit Constructive(8-11)
Weak Cue-bid No Mjr, no stopper
4 of other major, no stopper
3S aft 2H Invitational
4 spades, stopper, forcing
3NT Natural Stopper after 2H shows doubt
After 2S shows 4 hearts (Now 4D transfer to 4H)
4C Strong Invitation
Light invitation 4D
Strong Invitation Game force Jump cue-bid 5-5 minors,
4NT asks 5-5 minors; slammish responder to pick 4 of other Mjr to play
slam try 4NT Blackwood Natural
We also play over wk 2's cue-bids show a strong one-suited hand looking for 3NT Jump to 4/minor=2 suited, minor and other major (over major) over 2D-4C,4D asks major.