Learn Italian: Non le lasciamo neanche comprare il telefono nuovo!

This is a crucial rule for constructions using lasciare (to let) or fare (to make) plus an infinitive. When the second verb (comprare) has a direct object receiving the action (il telefono nuovo), the person performing the action must be an indirect object (le, meaning "to her"). If there were no direct object, you would use the direct object pronoun la instead, for example: Non la lasciamo uscire (We don't let her go out).

Why do we need both non and neanche?

Italian frequently uses double negatives. When a negative word like neanche (not even), mai (never), or nessuno (nobody) is placed after the verb, you must also place non before the verb. They work together to form a single negative idea rather than canceling each other out.

Could I attach le to the infinitive and write Non lasciamo comprarle...?

No, you cannot do that here. In permissive constructions with lasciare plus an infinitive, object pronouns must go before the main conjugated verb (lasciamo), rather than attaching to the end of the infinitive.

Doesn't lasciare normally mean "to leave"?