Standard AU, with Ereinion reincarnated mid-second age. I didn't intend for this to be a crackfic, but if you want to think of it as such, go right ahead.
Lord Elrond of Imladris did not like to be touched at any time, for any reason. A simple hand on the shoulder in greeting, or on the arm after a disagreement, by someone who was not a relative or close friend would be met with a step away from the contact and a please keep your hands to yourself.
When Merry and Pippin saw Elrond and Ereinion speaking together in a corridor, they watched with interest as Ereinion reached up and touched Elrond's cheek. Remarkably, the touch was welcomed, leaned into. The hobbits exchanged a glance.
They were definitely lovers.