The downside of Lebensohl is that you do have to remember some things about it. It's good to go over it several times and to practice.
You differentiate between the two by whether you have a stopper in the opponent's suit. If you do not, you bid 3N directly. This is known as "fast denies," which is a part of the convention card that you can check. Partner will know that you have a good hand, but no stopper, and can pull the 3N bid if he/she feels like it. If you do have a stopper in the opponent's suit, then you bid 2N, and then 3N over partner's 3C bid. That's the "slow" bidding sequence, which shows a stopper in the opponent's suit.
Similar to the above is when you have a good 9 count or better, no five-card suit, but a four-card major (that is not the opponent's suit). You'd like to push toward 3N, but you also would like to explore a 4-4 major suit fit so you can be in four of that major. Since the opponents have bid, you cannot bid 2C for Stayman. Instead, you use the opponent's suit to bid Stayman. Suppose righty has overcalled 2H. You can bid 3H to show a game forcing hand with four spades. However, what if partner does not have four spades? Then what? Well again, Lebensohl with "fast denies" can help you.
If you have a good 9 count with four of a major, you bid the opponent's suit directly if you do not have a stopper in their suit. If you do have a stopper, then you bid 2N, and then bid three of the opponent's suit after partner's 3C bid. That shows "Stayman with a stopper," and partner can act accordingly.
That's it for Lebensohl. I'll give you some examples of "fast denies" and Stayman bids:
S 6
H A7
D AK7543
C T653
Partner opens 1N, and righty bids 2S.
S K84
H KJT9
D QT9543
C
Partner opens 1N, and righty bids 2C (natural).
S T52
H KT842
D 65
C T75
Partner opens 1N, and righty bids 2D.
S 942
H 2
D KQT96
C K985
Partner opens 1N, and righty bids 2H.
S KQ52
H K982
D 86
C Q75
Partner opens 1N, and righty bids 2D, alerted as showing diamonds
and a major suit.
S T74
H AT75
D A43
C J42
Partner opens 1N, and righty bids 2H.
S AKJ943
H 42
D JT73
C Q
Partner opens 1N, and righty bids 2C, alerted as showing
a long suit, requiring lefty to bid 2D.
S QJ9
H A9862
D 2
C Q732
Partner opens 1N, and righty bids 2C, alerted as showing
a long suit, requiring lefty to bid 2D.
S 84
H 74
D KJ87642
C 82
Partner opens 1N, and righty overcalls 2S.
S 8
H KQJ
D KJ87642
C Q2
(You are south):
S AQJ5
H 643
D Q62
C KQJ
S K87 S T9432
H Q852 H KJT9
D J9 D T8
C 9874 C A2
S 6
H A7
D AK7543
C T653
(you are north)
S K84
H KJT9
D QT9543
C
S T52 S A9763
H 84 H 653
D AK D 876
C KJT752 C 83
S QJ
H AQ72
D J2
C AQ964
(you are north)
S T52
H KT842
D 65
C T75
S QJ9 S 643
H 953 H AQ
D KQJ743 D T2
C K C QJ6432
S AK87
H J76
D A98
C A98
S 942
H 2
D KQT96
C K985
S AQ3 S TJ875
H KQT96 H A4
D 5432 D 87
C 9 C J643
S K6
H J8753
D AJ
C AQT2
You want to bid Stayman here, but the question is, do you show a stopper? You do not have a diamond stopper, but you do have a stopper for whatever major righty has. The answer is you show stoppers in the opponents' known suit. So you should bid 3D directly as a Stayman bid without a diamond stopper. Frankly, that bid implies having stoppers in the majors, so if partner has diamonds stopped and no four card major, he/she should be safe bidding 3N. In this instance, partner will bid 3H and you will happily raise to four. Making four or five.
S KQ52
H K982
D 86
C Q75
S AT93 S 764
H J5 H 643
D KQT75 D J3
C 98 C KT432
S J8
H AQT7
D A942
C AJ6
2H is certainly down (2 spades, 2 hearts, one diamond, one club). You may get it two if you can avoid letting him park a club on a diamond or spade. 3N should make as well.
S T74
H AT75
D A43
C J42
S 82 S QJ653
H KJ8932 H 4
D Q9 D K8765
C KT5 C 63
S AK9
H Q6
D JT2
C AQ987
(If you and your partner play "Texas Transfers", discuss this hand and auction. You'll note that 4S is ice cold when south plays it.)
S AKJ943
H 42
D JT73
C Q
S T65 S Q8
H AQ963 H T8
D A9 D 6542
C 642 C 98753
S 72
H KJ75
D KQ8
C AKJT
With her 4333 minimum, partner will pass, and it will be challenging deal.
S QJ9
H A9862
D 2
C Q732
S AT3 S 876
H K H T354
D KQ9874 D T53
C K65 C JT8
S K452
H QJ7
D AJ6
C A94
S 84
H 74
D KJ87642
C 82
S KT9753 S 62
H KQ2 H AJT5
D 93 D T
C AQ C J97653
S AQJ
H 9863
D AQ5
C KT4
S 8
H KQJ
D KJ87642
C Q2
S KT9753 S 62
H A4 H T752
D 953 D T
C A8 C J97653
S AQJ4
H 9863
D AQ
C KT4