Though if you have enough users pinging the server you'll probably end up with a bunch of operations happening, which do have fees. It may be better cost-wise to just put this SQLite database on D1 (especially if it gets read-only replication at some point) and set up a Worker to return tile data in one HTTP request. That way the infrastructure is still serverless, but doesn't require N requests per tile, just 1.
(I also work for CF)