How long will vacuum sealed grilled lemons keep in the refrigerator?
Vacuum sealing food does not make it safe at all. You have to treat it like any other cooked food, only with the added risk of botulism. 

I was looking into whether your lemons might be acidic enough to be treated as a refrigerator pickle. I could not however find anything to confirm that. Worse, newer studies recommend against previously used "tried and tested" refrigerator pickle recipes due to listeriosis danger. 

So no, it is not safe. You shouldn't store it for longer than 5 days.