Falstaff is of course an old man who still acts like he's young, so calling him an "old lad" makes sense. Also, there was apparently a brothel in Shakespeare's day that was known as "The Castle," and given what we know about Falstaff, the old knight was likely a frequent visitor.
There is probably something else going on here, too, though. One of the big influences on Shakespeare's history plays was an anonymous drama called The Famous Victories of Henry the Fifth. In that play is a character named Sir John Old-castle, often called Jockey, who appears to have been the inspiration for Falstaff.
Why then, isn't Sir John Falstaff just called Sir John Oldcastle? Well, in all likelihood, he originally was. The historical Oldcastle, also known as Lord Cobham, really did know Prince Hal, and fought for his father, Henry IV. Once Hal became Henry V, he protected Oldcastle, whose heretical views landed him on the wrong side of the Catholic Church.
Eventually, however, even the king had trouble protecting Lord Cobham. Henry V had him imprisoned in the Tower of London, but he escaped. The historical Sir John Oldcastle then turned on the king and led a rebellion against him, hoping to have himself set up as regent and rule in his place. The rebellion was suppressed, but Oldcastle escaped and remained a fugitive for many years.
When Sir John Oldcastle was at last apprehended, he was tried, convicted, and sentenced to death. According to Holinshed's Chronicles of England, Scotland, and Ireland--a source Shakespeare seems to have frequently consulted in writing his history plays--Oldcastle was "hanged in a chain by the middle, and after consumed with fire, the gallows and all. Knowing that makes all of the references to hanging and burning in the Henry IV plays take on greater resonance.
Why, then, did Shakespeare change the name? While Oldcastle was deemed a heretic in his own day, by Shakespeare's time many regarded him as a martyr. That's certainly how he is portrayed by John Foxe in his pro-Protestant propaganda Acts and Monuments, generally known as The Book of Martyrs. Foxe goes as far as to compare Oldcastle with Christ, and calls him "this valeaunte Christen Knighte, syr Ihon Oldcastel," which is certainly not how we think of Falstaff.
The present-day Lord Cobham and his family must not have liked having their illustrious ancestor portrayed as a drunkard and leacher who robbed travelers and pretended to be dead to escape having to fight. By the time Shakespeare's play was published in a quarto edition in 1598, the name had been changed to Falstaff.
Why Falstaff? Well, Shakespeare had already made fun of another historical figure, Sir John Fastolfe, in The First Part of Henry VI, portraying him as a coward. If the fictional Sir John got confused with that other historical figure, it would be no big deal.
When he got to the end of The Second Part of Henry IV, Shakespeare added an epilogue that includes this passage:
One word more, I beseech you: if you be not too much cloyed with fat meat, our humble author will continue the story, with Sir John in it, and make you merry with fair Katherine of France, where, for anything I know, Falstaff shall die of a sweat, unless already he be killed with your hard opinions; for Oldcastle died a martyr, and this is not the man.
As it happens, Shakespeare did not bring Falstaff back in Henry V, but he does recount his offstage death in that play. The epilogue's claim that "this is not the man" could be a final reminder that Sir John Falstaff is a creation of fiction, and should not be interpreted as anything else.
