Hello ,
Normally the Loopback filter to lockdown management access works in "Input filter" and should not impact any traffic generated from the firewall to outside . Since DNS is generated from Firewall to outside , it will only check for any output filter on loopback/external interface . So this management filter should not cause any impact for DNS originated from the device .
If you are worried about the return packet from DNS server to the SRX , probebaly you can add a filter term to allow UDP 53 .