Although the i386 processor does not really have an L-flag, we can conceptually think there is one. The L-flag is important because it indicates ordering when signed numbers are ordered.
The previous two sections already illustrated how the S-flag and O-flag are not sufficient to indicate order when signed numbers are compared. However, when these two flags are combined, they can be used to indicate ordering. Let us define L = O + S. In other words, L = O ⊕ S (the exclusive-or of O and S).
Let us think about this in intuitive terms.
O = 1 means that although the sign flag is cleared, it is wrong. Since the sign flag can either be cleared or set, it means the sign flag should have been set, or that the result of the subtraction/comparison is negative (and we just don’t have enough bits to store it).
S = 1 means that the sign flag is correct, and it is set. This directly means the result of a subtraction or comparison is negative.
In both cases, the L-flag is set iff the result of a subtraction is negative. In other words, if the pseudo instruction is cmp x,y, then L = 1 ⇔ y - x < 0. This makes sense because y - x < 0 is equivalent to y < x.