https://remoteok.com and https://nomadlist.com both use SQLite as the database. 100+ million requests a month and there's been no problems.

For what definition of "large"? SQLite surely has no problem holding gigabytes of data or millions of rows. In many cases it's much faster than most other kinds of databases. So, size is not the problem. Throughput on one machine with one active process on the same VM is not the problem. Having multiple processes on one VM in most cases is no problem.

But if you spread your compute across many machines that access a single database it can get iffy. If you need the database accessible through network there are server extensions which use SQLite as storage format but you're dealing with a server and probably could use any other database without much difference in deployment&maintenance.