All current HP switches support LLDP.
HOWEVER:
I've never seen a Cisco product (routers, phones, switches, etc) support LLDP, and from what I have heard someone waiting for LLDP support will have to wait quite a long time.
Based on my experience, if you want a Cisco phone to correctly autodetect the separate VLANs for voice & data, you will need a Cisco PoE switch to connect it to.
There may be a way to configure the VLANs in the phone's config file using the native "skinny" firmware, but there is most definitely NOT a way to do it on a phone using SIP firmware.