IMO, this makes sense when you consider the self schema and psychological defense mechanisms. These include things like projection (placing your own unacceptable thoughts on to others), displacement (directing emotions at a substitute person), denial, rationalisation (making up acceptable excuses for unacceptable behaviour). They are strategies used by the mind to manipulate, distort and deny reality to cope with negative emotions and to maintain the self-schema. The self schema is all of your beliefs about yourself, your life and the people in it.

The LSE is just one manifestation of this behaviour. A woman who is perfectly happy in a long term relationship might believe things like "I am a good person", "I am loyal", "My partner is amazing" but if she were to feel attraction for someone else, she would become conflicted because it would contradict her belief that she is loyal. Her mind will need to utilize any number of the defense mechanisms to cope with this. It might be that she gets angry with herself but directs the anger at someone else (displacement). Or she might accuse her partner of being unfaithful (projection). She might try to rationalize it by convincing herself that the relationship isn't that great and she's been unhappy for a while (the LSE).

If the guy were to catch her before she has finished the rationalisation and he dumps her or tells her he wants a divorce, her initial reaction is often to beg for forgiveness and to say she will do anything. She still believes that her partner is great and him dumping her / threatening divorce would conflict with her "He is dependable / will always be there for me" belief. Panic will set in resulting in the begging and pleading.