When I have had this issue, the problem has been no DNS defined in [IP -> DHCP Server -> Networks] for the relevant network.
Ok. I've set my dns-server to 10.10.10.1 so hopefully this is correct. When you set yours up, did you have to append firewall rules at all?
10.10.10.1 looks about right. I needed no firewall rules to 'make things work', but I did need some to isolate networks.
I've finally managed to get internet on my VLAN 
. In the end, it was firewalling rules, I had to add my VLAN "management" into the list member LAN as the firewall filter was blocking all incoming traffic not from LAN.
I probably still have a lot of cleaning up to do to actually isolate it but I'm pretty chuffed to have it actually working! You are real AF for sticking with me through this so thanks!
In most cases its easier to include the vlan management interface or subnet etc, to the LAN list and thus has immediate access to whatever the LAN has, be it DNS, or internet traffic.