Are you travelling in from Lincoln?
I used to do this from Oxford and there was an excellent bus service that I picked up on its last stop out of Oxford at the park & ride (free to park). It ran 24x7 (clearly not as regularly during the wee small hours) directly to T5 and then to the central bus station. It was about £10 each way I think.
My recommendation would be to find a similar service down your closest motorway and do it that way. Unless you fancy opting for trusting your car to a cheap (= dodgy potentially) far-offsite parking company.