http://www.thespacereview.com/article/739/1
JFK just did propose a joint manned lunar program in September 1963, in a speech in front of the U.N assembly. Because he was shot only two months later, the proposal remains an enigma even today (also, some JFK papers are classified until the late 2020s or beyond, or at the will of the Kennedy family)
Even today, nobody (not even the best NASA or space historians)
really knows if
a) JFK really and sincerely believed a manned lunar program could be done with the Soviets (looks like the idea popped after JFK met K. in Vienna in June 1963)
or
b) if JFK was afraid or embarrassed by the cost burden of Apollo he had committed into two years before, and intended to share that cost with the Soviets
What is sure is that once LBJ sworned in as president the proposal had no chance and was quickly buried.
Surely, it would make for one hell of space ATL. This is a very good POD in the early space race.
We can imagine that Apollo proceed with LOR (the decision had been made and frozen in September 1962, a year before)
I'd say the program could proceed as follow
- NASA keep building the Lunar Module (the Soviet LK stands no chance, it was a one-man tricky piece of junk)
- but the Apollo CSM is replaced by a Soyuz with a LM docking system which allows astronauts transfers without EVA
When I say replaced, it can be replaced as a whole (all Apollo missions use a Soyuz as the manned lunar orbiter) or just for a one-shot deal (as ASTP).
Placing a LM docking ring on the Soyuz wouldn't be too hard - ASTP had the Soyuz modified with a different docking system, Apollo remained untouched.
A major issue (with perfect post 1971 hindsight) is that early Soyuz were unreliable, Soyuz 11 carried three men (unsuited) but they died per lack of space suits, so Soyuz crew was cut to two suited cosmonauts from 1973 until Soyuz-T gets introduced in 1978. What is sure is that Apollo needs three astronauts, not two. So that might be a major issue.
Another major issue, of course, is the N1 troubled flight history.
But imagine if a Soyuz was placed within the Saturn V shroud, just like an Apollo CSM. It would pick the LM just like the CSM did (180 degree turn). The lunar Soyuz was one-third the mass of a CSM - 10 tons versus 30 - so the excess Saturn V payload could be transfered to the LM, with knock-on positive effects.
Then there's the issue of the escape tower, but it was one out of few components of the Soviet lunar stack that worked correctly - most of the time the N-1 exploded, the escape tower pulled out the Soyuz crew module to safety.
A Saturn V with a Soyuz escape tower on top would look a bit strange, but there's no reason it couldn't work. Overall, Soviet and American electronics are of course different, but with a POD as of late 1963, they have five or six years to provide for compatibility.
For the record, ASTP was decided in May 1972 and flew in July 1975 - a bit more than three years.