I wouldn't summon her. Not because she's bad [I actually like the tale of Lilith] but because if you're worshipping or calling on her for a spell, it's better to grow closer with her and build a relationship. Summoning is basically demanding someone to be there, and Lilith might be a little upset at you and wish to teach you a lesson. So I suggest the worship route.
Get an offering for her [something she favours] and set up an altar dedicated to her. Say a prayer and ask her if you could learn from her. Meditate and wait for an answer. This could come in a few ways so be open. It can also take some time, if you get a no [or no answer after a month] thank her and move on for a bit. If she says yes, you can begin working with her. Prayer, offerings, calling on her in circle, meditating before the altar are some ways to grow closer, but you can find other ways to worship her.