Ok, thanks for the edit (re ‘he was not a Tory’), but re “come in handy in a close vote”, TBH she would never have had any leverage over his vote, either, other than on unwhipped votes which by their very nature no governing party leader cares much about - all votes that matter are whipped and a Liberal going against his party whips’ instructions to vote with the Tories would have stuck out like a sore thumb.
(As an aside, if he HAD been a Tory, then he would not have needed to be knighted - no carrot needed - the whips would simply have let him know that THEY knew, and with this stick his utter loyalty would have been a given on pain of a leak finding its way to the press if he ever even thought about stepping out of line. That’s real House of Cards (the original) territory.)