I assume the lagg settings must be correct since it works after re-saving.
It does seem like some issue at boot caused by the delay setting up the lagg I agree.
We need to determine exactly what has failed when that happens.
If the WAN/lagg has a valid public IP and the default route shows the correct gateway then I would expect to be able to ping out from Diag > Ping for example. Even if Unbound (the DNS resolver) fails to start the system itself should still be to ping by IP, to 8.8.8.8 for example.
You may not have the required automatic outbound NAT rules preventing LAN side clients connecting. Check Firewall > NAT > Outbound.
Check the system logs after rebooting. I suspect what you will see is that when the WAN connects and gets an IP it is ignored because it happens during the later bootup process.