OED’s first print citation is Hy Lit’s unbelievable dictionary of hip words for groovy people (1967), which defines do a number as “to get mad; make a scene; to tell somebody off; blow your cool”.
This is likely a figurative use of the show-business idiom do a number meaning “perform a stage act”. (Compare make a scene.) OEtmD traces its origin to the printed performance bills for variety shows in the late 1800s, on which each act was marked with a number. (For an example of such a bill, see the “Vaudeville” entry in Wikipedia.)
But OED adds that do a number (on) has acquired a more general meaning over time: “to act with destructive force or impact; to criticize or humiliate; (hence) to have a strong, usually adverse effect”.
Consequently, the excerpt in question means that Lisi blames Jerry’s mother for damaging him emotionally, thereby contributing to their relationship problems.
The idiom does not imply that Jerry suffers from a specific kind of emotional disability such as fear of commitment. The montage scene is simply a collection of statements that are stereotypical of lovers’ quarrels. The scene implies that Lisi and Jerry absurdly spent nine hours playing out every possible lovers’ quarrel stereotype. The humor of the scene derives from this absurdity.