Going by the title, I think Superninja76 was asking what would have happened if Baldwin hadn't contracted leprosy in the first place, not just what if he had lived a bit longer.
Ah, I guess I mssed that.
It's significantly harder to answer, giving that he contracted leprosy really young : it would likely change significants features of his reign, personality, etc. So while we could argue that it would make him a better or a worse king without much to contradict either, I'm going to be relatively vague, and more focused on geopolitics rather than how *Baldwin IV would directly change history.
First, Ayyubid takeover of Egypt and Syria is a given ITTL. Meaning the whole set of military pressure, harassment and threat of reconquest is still there, and it's not something easy to deal with. While during Amaury's reign, Latins could count on the important rivality between whoever controlled Egypt and whoever controlled Syria, this strategy is moot then.
The big changes would be about the Yerosolemite Kingdom, eventually.
We could argue that Amaury would live longer than IOTL, due to the absence of stress knowing his successor contracted leprosy (an illness that, for what matter medieval public opinion could be compared to the perception of AIDS in the 80's), possibly allowing a smoother succession.
I do think, tough, that Amaury's expedition in Egypt isn't really going to work out, probably significantly less so than the expedition of 1167-1168 before the clear hostility of the population, the Ayyubid control (altough Saladin doesn't have control of Northern principalties) and general weariness of Latin resources (the Armenian expedition wasn't exactly stellar). At best, tough, I could see it as a successful raid.
The lack of more or less constant intrigues around Baudouin, due to his sterelity and his incompetency (in the medical sense) is certainly going to embetter the political situation of the kingom, making it more unified. It's a relative observation, tough : the Yerosolemite Kingdom was concieved as an idealized feudal entity, with a top-down/down-top vassalic relationship, meaning that the great feudataires had a large independence from the crown, and even vavassors (vassals of vassals) could intervene in the High Court (which shared much of the rulership with the king who, at times, was stuck with a more or less purely redistributive, military and of course vassalic role).
The interesting part there is which alliances Baudouin would eventually favour : it would certainly go with a matrimonial union. Now, I know that medieval match-making is one of the best way to have a teraload of posts in pre-1900, so I won't spoil anyone's pleasure. I'd just point that such alliances were generally searched for possibility of military support.
A new alliance with Byzzies seems a bit overstretching, especially giving the latter reign of Amaury, and the familial closeness (such marriage could be frowned upon due to cosanguinity as defined trough clerical perception).
An alliance with Montferrat still seems likely, due to their ties with Capetians and Honestaufen, with a union with one of the three daughters of Guilhèm V, instead of a marriage with the IOTL Guilhèm Lungaspada. One could argue, tough, that this union would be particularily anambitious.
But few of Yerosolemite marriages were really about trying directly with great lines after all. If not Montferrat, then maybe Bourgogne with an union with Mahaut daughter of Eudes. The point is that it would search support among French and Imperial nobility.
Now, as said above, I do think that Saladin is still going to have the upper hand on the conflict with Latin States by sheer ammount of ressources, political strength and skills. Maybe ITTL, tough, a safe and sound king that can assume the military function of his charge, and with a significantly (if not wholly, as pointed above) realm might simply do better, and avoid giving Saladin too much opportunities.
The whole pressure on Latin States since decades, a pressure that will go growing, would still ITTL lead the kingdom in deep crisis up to a *Third Crusade IMO. But with a significantly better hold for Poulains and Crusaders (in the same time, it's not that hard to think of a better hold than IOTL Third Crusade situation), it just might turns out better. Possible no civil war, more unified Poulains and more territory are good assests : we might even see a recapture of Jerusalem ITTL.