I’ve heard of people using a shared Gmail account for support tickets and handling ownership with labels.
I'd certainly recommend this approach, especially if your workflow is well defined (we answer, then archive - Follow Up and start a ticket in Lighthouse if it needs to fixed. Unread == unanswered).
Have looked at ZenDesk and Tender, but we feel like they force people to jump through too many hoops in order to ask a question. For a logged-in user, it should really just be a "what do you want to ask us?" field, and for a logged out user just email/question. In my humble opinion, of course. ;)