Linseed oil is what is known as a "drying oil" meaning that it actually sets if exposed to the air to form a hard film (it's used in oil paints for this reason). I don't believe lemon oil does this (or olive oil either).
I guess you could argue that it might help the fingerboard to have a hard, linseed oil film set on it but I'd want to check first before using it.
i think that depends if you are using 'raw' or 'boiled' linseed oil. as far as i am aware raw oils are the non-setting ones
personally i prefer an oil that would set
on the wood, because it also sets
in the wood. I will coat dry rosewood fretboards with a little danish oil and quickly buff it off. this prevents it building up
on the wood but ensures enough soaks in and sets to provide protection and reduce the need for frequent re-oiling sessions
but then i only do this on the dryest of boards. most get cleaned with the 0000 liberon wire wool and thats it