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Unless you have evidence that the name was originally Lowton it's best to assume it was Lawton. Lawton is the commoner English surname, also Lawton is on record in Ireland, I'm not sure Lowton is. Anyway both English place names and surnames mean the same thing, a farm near a "law", or hill.
In Ireland, it seems, Lawton has been used sometimes as an English language substitute for Ó Lachtnáin. This name seems to have caused English speakers much trouble, and they made it Laughnane, Loughnane, O'Loughlin (a different surname), and even Loftus in Co. Mayo.