If the work at the lab was in any way related to your course, such as part of a placement or project you get credit for, then I would include the university's logo.
However, if the university was in no way involved, for example if this was a summer project that you found independently, then the university's logo probably doesn't need to be on the poster.
In any case if you are unsure then the best idea is probably to talk to someone who was involved in the project and possibly also someone from your university (your personal tutor or similar). They will be best placed to advise you for your particular situation.