Potential advisor offering to fund visit to lab

I do not think the etiquette you are talking about applies here. You need to go there in order to ensure compatibility between you and your potential future advisor. This is neither a gift nor a present; it it a business related trip and I do not see a reason for not agreeing to this.

Be glad for the offer and accept it. The advisor's LAB will cover the expenses, not himself. It is possible that he or his team have a budget where things like this are included. He probably has money that can be spent only on research related stuff, like funding the stay of a visitor or future research collaborator.

Refusing funding is unjustified, unless you have funding of your own. But even if that's the case, he made the offer so just accept it. A polite thank you is enough.