Why does time machine cause my Macbook Pro to crash?

Welcome,

You may be better placed asking this question in the Lion Forum. Also there were known issues with TM in earlier Lion version - if your sig is correct you may want to try and update from 10.7.3 to 10.7.5.

Also it may depend on whether you are using a directly attached disk or a Time capsule (if the latter there is also a Time Capsule forum)

Regards,

Shawn