Same as above. I tried mostly unsuccessfully to get into the lobby and the one time I did I was disconnected! It was the same after 7pm in another lobby too.
It's definitely a sluggish network problem. Outside of GT6 the logging on, friends list populating and their avatars appearing was again very slow.
I think there are problems on the PS4 but I do wonder if it's quite so bad on the paid for network. If I hadn't gone and bought a G29 in the sales I might now be considering an Xbox one!
Edit - I've just spotted this so there might be hope..
Scheduled maintenance reminder
Affected Platforms:
PS4™ , PS3™ , PS Vita , Web , Other
Affected Services:
Routine maintenance and improvements for PlayStation™Network will be performed for approximately 2 hours between 02/03/2016, 05:30 and 02/03/2016, 07:30
Start:
02/03/2016, 05:30
End:
02/03/2016, 07:30