Intermittent network / routing problem - don't know where to start

Don’t think of myself as a newbie but neither an expert. I’ve got an intermittent networking/routing problem which I don’t know how to troubleshoot.

There are certain websites (large well known) that I cannot access from my LAN. I’ve tried from my mobile device and the sites are up. It’s only a small number of sites where I ran into this problem. The connection from the browser times out.

I cannot ping these specific sites (DNS is working fine) from the LAN but can ping them from the router. Running a RB4011 and just updated to 7.10 but was a problem before, no exotic config on the router. Happy to post the config if that helps but personally find reading through somebody else config sometimes a bit painful.

Would appreciate some guidance on how to troubleshoot.

I would search for some weird NAT rule or mangling.
You can also trace network flow from your laptop in LAN (tracert facebook.com for example) and see where it stops - on your router or somewhere behind.
It looks like something like UTM behind you which drops connection from your LAN but not from your router. Are those two separate VLAN’s in your environment?