Career
Ashcroft made his debut for Kilmarnock on 11 May 2013, as a substitute in a 3–2 victory against Dundee in the Scottish Premier League and then four days later scored his first career goal in a 3–1 loss against Hibernian. On 14 May 2013, Ashcroft signed a new contract with Kilmarnock, keeping him at the club until 2016. On 4th April 2015, Lee made his captaincy debut, at 21-years old, captaining Kilmarnock to a 1–2 defeat to Motherwell at Rugby Park.