You have two choices: Those who believe the name is Welsh and have Welsh-English dictionaries say "where water rushes down a flume". Unfortunately no Welsh speaking person believes the name is Welsh. It is probably English and appears all over English records from about the 16th Century on and from the Midlands down to Devon. Big concentrations in Midlands, London and Devon. That origin suggests something like Lynns valley or Lynnscombe. Variants get the extra syyllable out of the middle s and it can be Thi, The, Te, Ci, Si or whatever. The original Thomas Linthicum came to Maryland in 1658 and called himself Linscombe, when he registered some property in the 1660s he was Lincecombe and when he died he was Linthicum. There is at least one other family that traces through French origins and uses a Lincecomb variation on the name.