Can a chalazion on my eyelid be lanced at acute care?

I would not have a chalazion treated at an urgent care center. I would see an ophthalmologist or ophthalmic plastic surgeon for treatment and/or removal.

This would depend highly on the experience of the physicians. It is very uncommon that a doctor at an acute care facility would have much experience in draining a chalazion. The possible complications that can result if this is done incorrectly are significant.  I would recommend seeing an ophthalmologist at the very least. An oculoplastic surgeon would be even better. We see several of these a day. The cost involved would likely be the same since the same procedure codes would be billed, in case that is a consideration.

An acute care center will usually refer a chalazion to an ophthalmologist for drainage.  Best of luck.