I am trying to help a friend determine if a warforge has a soul because their character has died and wants them to be brought back with resurrection magic. Since resurrection magic requires a soul, do warforges have a soul that can be brought back?

Since Warforged are humanoid, they can be brought back to life with revivify, raise dead, or similar magic. You don't need to debate over whether or not they have a soul.

Okay, but what is the lore reason? Because everywhere I look I can't find a definitive answer. Or is it supposed to be ambiguous?

I believe it's supposed to be ambiguous/up to the DM.

In my campaign Warforged where created after an accident. A Githzerai wanted to forge an army of autonomons, she saw that faced against the military might of the Githyenki and wanting to continue the war with the illithid she found ancient forgotten lore regarding the creation of mechanical constructs. 

But when she performed the ritual to activate the 2000 warriors something went wrong, maybe some translation she misunderstood, or maybe because she performed the ritual in limbo itself and pieces of soul a course to each, but when the spell was complete she had 2000 sentient self aware true new beings, like children in wisdom and experience but fully formed strong able to fight. These warforged do have a soul, ripped from limbo, unaware of who it was before now only identified as the soul forged that it is 

I would say for ease of game mechanics, and because I find the RP concept of a (fantasy) robot with a soul really rich and interesting, I would lean on the "yes, they do" side.

It is a very philosophical discussion. What is a soul, in your world? Is it something you are born with and that's that, or is it something which you can grow from nothing through your actions? Most stories and films which touch on this through emotional feelings - when something stops performing every action through logic and starts to experience feelings, then that is when it develops a soul. A machine might still >feed the birds because they require sustenance<, but if it experiences a flutter of joy when a bird lands on its hand, even if it doesn't understand it, then it is developing a soul, at least in part.

I prefer the idea of the latter. I also like the way that this leaves potential for less sentient warforged (the ones who just follow orders) to be possessed by the souls of others as they are blank vessels, like how the ghost doctor possessed the warrior from the golden army in hellboy 2. I may even elaborate this into a character some time, a warforged with a mortals soul in command, perhaps learning of it's previous life as the campaign plays out, finding out why it was trapped in this metal body...

Or a warforged who is determined not to develop a soul, as only those with souls can be judged by gods, so is in denial about every feeling they experience... "I am not a caring individual, I am a cold, hard automata! Stop making me feel good about saving you!".

hmm...

Depends on how the particular DM wants to handle the more philosophical concepts of a creature's soul as well... Traditionally, most versions of D&D have viewed "souls" as being a spiritual representation of the particular individual that travels to the Outer Planes (or elsewhere depending on the circumstances) after death. However, perhaps a warforge follows a more Buddhist concept that their soul is more an extension of the universal energy around us (i.e., similar in concept to what to Scarloc mentions above). 

Personally, I would probably go along this general route myself as a DM. Yes, each warforge has a life energy and a soul, but this soul is more of a living embodiment of the universal energy than an individual spirit.

I mean the machines used to create them are called soul forges/creation forges.

Would a devil do a deal with a warforged? That would be a great political adventure in hell, warforged soul is sold by its creator and the party go to court to argue that as the warforged has no soul it can’t have been sold in the first place. 

And the barrister of Hell provides exhibit A, the Warforged soul, in Infernal custody persuant to a Writ of Detention filed as soon as this nonsense appeal was lodged with the court.  Hell moves claimants be held liable for Hell's attorneys' fees, to be rendered in the form of their souls. <gavel>