Lebensohl vs 1NT

2NT response (when 1NT is overcalled): Artificial transfer bid, forcing opener to bid 3C. After 3C relay, responder may pass (with clubs), or bid three of his suit as a signoff.
3 of a new suit (after a two-level suit overcall): Natrual and forcing.
Double 2-level overcall: Penalty with 7HCP defensive strength.
Double 3-level overcall: Takeout.
Cuebid: Stayman. It promises at least 1 four-card major and denies a stopper in the enemy suit.
3NT: Denies a stopper in the enemy suit. opener pass with stopper in enemy's suit, or explores for a better contract.
2NT then Cuebid: Stayman. It promises at least 1 four-card major and promise a stopper in the enemy suit.
2NT then 3NT: Promise a stopper in the enemy suit.