Sie hat sich gestern von ihm scheiden lassen.
This sentence uses the infinitive lassen instead of the perfect participle gelassen. Which grammatical rule causes this?
This is the so-called Ersatzinfinitiv. It is used with the following verbs:
Depending on the dialect, fühlen and helfen can be added to the list.
For details, check out e.g. Zwiebelfisch:
It's a passive action, in German (as well as in English(?), you don't "divorce", you "get divorced".
Also, the word "hat" is the past tense form of "haben", so the past tense is already defined in that statement and "lassen" can and must stay in the infinitive form.
This seems to be always the case when the supposed participle (e.g. lassen) goes with an infinitive (e.g. scheiden).
Most of the concerned verbs are "Modalverben" in German and follow this rule (have a look at mein-deutschbuch.de).
So, you might say that lassen is used as a "Modalverb" here.
Here a very common example from a children's rhyme:
Now, I finally understand that the point of this rhyme is practicing this exception.