There doesn't seem to be any major storylines for Finn Barton at the moment. He is just included in minor scenes as one of the characters within the general comedy set (Jimmy, Nicola, Rodney, Kerry, Bernice, Marlon and Paddy).

Finn graduated from university around 2013 but has since stayed in Emmerdale in mainly unskilled paid work. One reason for not leaving Emmerdale for a better life is known to be shortage of money. I'm guessing that he may have an outstanding student loan too. He has had various gay relationships and one-night-stands with mainly young men (Simon, Brad, Aaron) up to 2014 but no-one during 2015 as of yet. However, he did previously have short-lived crushes on the older straight characters of David (then 31yo in 2013) and Declan (then 45-46yo in 2014) but these didn't last for long. With this history, it seems unlikely that Finn would be sexually attracted to Lawrence. Except for Robert, there doesn't seem to be anyone of the right type for Finn to have a relationship with within Emmerdale so a young man from outside Emmerdale is needed for a workable storyline lasting for more than the short-term.