The LLDP-MED Network-Policy TLV feature may be used to communicate some combination of VLAN, Priority, and/or DSCP value to an LLDP-MED-compliant IP Phone:
How To Configure LLDP-MED (Network Policy)
How to configure LLDP on a Securestack
I see that CEP (Convergence End Points phone detection) support was added as of v6.71 but I have yet to see a CEP configuration outside of the Config Guide.
If seeking to do more - perhaps using CEP or Policy - the possibilities multiply so a more in-depth conversation is needed. I'd be happy to open a GTAC Support case on your behalf for that purpose, if you'd like to take that approach. Closing the loop in this Hub thread will be helpful to all, so is part of the plan either way.