David:
If the CPU load on your server is not changing much during these times you could be experiencing a network issue.
The only way to make sure is to collect some metrics, if possible from the server, if not from the same network zone your server is on.
Maybe something as simple as cURL + chron job or similar. You may have other tools.
My guess would be if by extending the timeout you fix things, then, most likely Lucee is waiting on network resolution. Your firewall could be busy, your connection spotty, etc. You will need to collect objective metrics to get to the source.
HTH,
Bilal