Currently the quest is in its 2.4 incarnation, and as Lord Solanar was added only after 2.4 and the world is in its original shape, you can't hand in the quest to anyone.
Lady Liadrin is currently in Silvermoon (as she should be in 2.0.3), the problem is in quest you receive involving an NPC that doesn't yet exist instead of her.
When M'uru was brought to Sunwell and Lady Liadrin moved to Shattrath in 2.4 patch, the mount quest A Summons from Lady Liadrin was altered a little and renamed A Summons from Lord Solanar.
Currently the quest is in its 2.4 incarnation, and as Lord Solanar was added only after 2.4 and the world is in its original shape, you can't hand in the quest to anyone.