This occurring before the adoption of the 25th Amendment has the potential to be a real Constitutional crisis if the heart attack is non-fatal but incapacitating. Johnson would be President, with the Speaker of the House next in the line of succession, with no provision at all for an Acting Presidency. This is all occurring, of course, in the middle of the Cold War.
Accordingly, you would have, in the case of a non-fatal but incapacitating LBJ heart attack a very real problem of nobody being able to exercise full Presidential authority or, in other words, a complete cluster****.
The scenario would unfold something like this:
1230 CST Kennedy shot by Oswald
1300 Kennedy pronounced dead
1315 (approx.) LBJ informed of Kennedy's death, suffers heart attack at Parkland
1320 LBJ heart attack diagnosed at Parkland emergency room, LBJ in critical condition and unconscious
1338 Walter Cronkite announces death of JFK and unconfirmed reports of incapacitating heart attack of LBJ
1400 US Government in chaos as word of LBJ's condition spreads; Attorney General Robert Kennedy left to sort out the legal mess. If he's lucky, he'll find some obscure provision of law to enable someone, probably McNamara, to take charge of defense/national security
1500 LBJ's condition revealed to public; it becomes readily apparent that the US has nobody in charge, with a good chunk of the Cabinet, including Secretary of State Dean Rusk still in the air after aborting a trip to Tokyo, adding to the confusion.