The World as Myth/WMG

Robert A. Heinlein did not die in 1988, he was rescued
The key concept of The World As Myth is that all fictions are real. Which, of course, includes The World As Myth books. With the Burroughs drive you can cross universes into other fictions, and in The Number Of The Beast the main characters are shown doing a last second swap: One braindead clone substituted for a near-death person, who can then be revived with their Sufficiently Advanced technology. With creators of long-lived fictions being incredibly powerful (since all reality is fiction, they can influence how universes develop), the Time Corps would want to get access to their own creator at all costs. So Heinlein provided his fictional characters with existence (All reality is fiction, all fiction is reality), means to rescue him from death, a motive to rescue him, even experience at doing this sort of rescue.
 * Plus he actually turned up, along with some other well known authors, at the Con at the end of The Number Of The Beast so there was direct access.

RAH did not die in 1988, He assumed the identity "John Varley"
"John Varley" is a pseudonym he established in the '70's so he would not get over-exposed in the mag Analog. Since it is plainly evident that Lazarus Long was an author stand-in, it is proven that the "Varley" thing is part of his Howard Foundation Masquerade. Really, people. Nothing could be more self-evident! Sure, some you may have met that actor with the beard at 'cons who claims to be "John Varley", but really ... ever seen him anywhere else?

Thought not!

And now for something about his actual fiction:

Lazarus Long was genetically engineered for longevity in the far future.
The setting has time travel and advanced biotech, and as Long himself points out, his unusual adaptations are awfully specific and systemic to result from random mutation...

Alternately, Lazarus Long's father is a time traveller from the future.
With the exception of the red hair, which is a trait from his mother, Lazarus seems vastly unlike any of his siblings or half-siblings in temperament and characteristics. Also, the genes of Brian Smith and Maureen Johnson Smith never produced anything like Lazarus' adaptations despite fifteen other attempts at combining them. Add in that Lazarus' parents had an 'open' relationship and Maureen was entirely open to sleeping with men other than her husband, to the point where Lazarus has at least one acknowledged half-sibling (Patrick Henry Smith, child of Maureen Johnson Smith and Patrick Weatheral), and Occam's Razor says that Lazarus' unique genes did not come from a vastly unlikely set of multiple independent mutations the odds of which were one in several million for any single mutation and one to positive infinity against when taken all together. They instead came from a unique parent, a visitor from a far future, centuries after even the founding of Tertius Colony, when such genetic traits are a near-ubiquitous presence in the human gene pool. As the origin of such traits in the far future human gene pool would be via virtually everyone alive at that time being a descendant of Lazarus Long (the logic of which is explained in detail by Justin Foote in the foreword to Time Enough For Love), we are then left with the ironic realization that this particular time traveller really was his own (great-great-great-etc) grandfather.
 * Of course, it seems likely that most of Lazarus's genes were pre-existing; he really does have a lot in common with his maternal grandfather Ira Johnson, to the point where said grandfather mistakes the adult Lazarus for his own (illegitimate) son. The differences aren't so much in personality or appearance as it is in whatever makes Lazarus eternally youthful instead of just being long-lived. So maybe Brian Smith is the father, and just happened to contribute the few key traits required to create true eternal youth in their son.
 * Then again, for all we know, Ira might be the child of a time-traveller. Lazarus' immortality gene is clearly a recessive, because his children aren't all immortal. So it takes a few generations before the "immortality gene" in the Smith family line gets crossed with another copy of the gene (from Brian Smith). At which point Maureen and Brian have an immortal child- but the recessive gene combination required is improbable enough that none of their other children get it. Fifteen is not a large number compared to the possible chromosome combinations from a human mating.

The world as myth is a gigantic Xanatos Gambit by a time traveller who found Heinlen's books.
Every event caused by the organization, including their own Xanatos Roulette plots, was one giant plot by an immortal time traveller from the Aldrin timeline, found Heinlen's books, and decided top see if he could set up the Harriman timeline, because it seemed interesting. He used copies of sentient human minds to make the computers sentient, placed things inconveniently or conveniently as necessary for the timeline to occur propely, and the Burroughs drive merely transports people to pocket universes that the Traveller created outsde of time. (Incidentally, every wall that Pixel walks through was remotely portal'd by the Traveller.)

Lazarus Long did die in that flophouse; the whole book is his Dying Dream
. It does seem rather wish-fulfill-y. He gets young, all women want him...
 * On the other hand, it's not like any of that isn't "justified" by events in his own past- he's been rejuvenated several times, and women have thrown themselves at him before. Moreover, many of Heinlein's later works involve the time-travelling organization that Lazarus is part of; for him to have died in that flophouse, several other books (like The Cat Who Walks Through Walls) must also be part of Long's Dying Dream... from the point of view of other people in the dream!