Can a car get towed from a private parking lot in a condo complex for expired tags?

it depends on the managment rules or policys.

The correct answer is look at the lease you signed. That lease is a contract. WHAT DOES YOUR LEASE SAY ?????? (my answer rests on the assumption that you are a tenant and have a lease; if you are not a tenant, you do not have a lease, therefore you are parked on private property and have voluntarily (knowingly or not) subjected yourself and your vehicle to whatever rules or policies exist upon that property)