His wiki entry mentions that he was a Nazi hunter at the end of the war.
What sort of work did this entail? Can the particulars of his missions be reconstructed from declassified records?
And there is also this:
"Lee mentioned that during the war he was attached to the Special Operations Executive and the Long Range Desert Group, the precursor of the SAS, but always declined to go into details. 'I was attached to the SAS from time to time but we are forbidden – former, present, or future – to discuss any specific operations. Let's just say I was in Special Forces and leave it at that. People can read in to that what they like.'"
The short answer is "probably not", at least right now. The most useful resource (at least for charting where Lee was posted, with which units and when) would be his military service record, but full individual service records are only available to next of kin until 25 years after their death — meaning it'll be 2040 before historians can get a look at Lee's. From the geographical info and dates in his service record, you could potentially start to build up a picture of what the unit he was with was doing at a given point in the war.
You could scour the wartime records of his parent unit (No. 260 Squadron, RAF) — they're held by the National Archives, but they're probably not going to shed too much light on an individual officer's specific wartime activities, particularly while on secondment to other units. Lee never claimed to have been member of the LRDG, SOE or SAS, but rather to have been temporarily detached to those units or assigned as a liaison officer.
Regarding the 'Nazi hunter' portion of the question — Lee was ostensibly attached to the Central Registry of War Criminals and Security Suspects (CROWCASS). You could go looking in those records for references to Lee; the National Archives and UN both have extensive holdings of CROWCASS records.
As is so often the case, the problem with more or less all of what I've suggested above is that most of these records aren't digitised, so there would be a lot of leg-work involved in searching them, and the most you'd likely find would be passing references.
I should point out that after Lee's death, one not-especially-notable historian made some headline-grabbing claims that Lee embellished his wartime record, albeit without much in the way of specific allegations or evidence. Make of that what you will...