So from my understanding, Sun Quan had a pretty good position in the Southland even before Red Cliffs. I understand that his land was stable, wealthy (at least in comparison to other lords), and the military was in a good state. He also had the natural fortification that the Yangtze provided for defense.
It seems like at the time Liu Bei only had what was basically a remnant force from his defeat in the Battle of Changban, accompanied by whatever forces Liu Qi brought with him from Jiangxia Commandery. Given his situation, It's hard to see what Liu Bei had to offer in the alliance. Even more strange to me is that it was a apparently an envoy from the Southland, Lu Su, who suggested the alliance to Liu Bei in the first place.
I've read the parts of the Sanguozhi biographies of Liu Bei and Sun Quan that speak about that battle, but it doesn't really give any information besides "They allied and fought and Cao Cao retreated and they chased him." Other than that source, I'm not sure where else I can look.
I'm not sure if my premise if flawed. But if not, my question is: Why was it important for Sun Quan to form such an alliance with Liu Bei to resist Cao Cao? Was there something crucial that would make it impossible to resist invasion had the alliance not been formed?
For future reference in terms of finding information on three kingdoms, individual SGZ of those involved can be more help then rulers. Nobody in Shu (records were notoriously bad) really covers Chibi well, Wei downplay it but the two big SGZ's for the build up and the war, I would suggest, are Zhou Yu and Lu Su. Another option (particularly if your not sure about which biography to look up) is the ZZTJ (the Chibi relevant section) which provides an overview.
Wu was, at that stage in time, not as powerful as perhaps you think. It was a provincial government away from the traditional centers of power, it had recent success in Jing and was making headway in the south but the economic strength and the great expansions were yet to come. Wu and Sun Quan's peak was yet to come, they were facing a man who controlled the traditional centers of power and seemingly on a roll.
There were plenty of doubts within Wu about the adventure, figures like the honorable Zhang Zhao suggested submission while long serving cousins on the frontier were doubtful: Sun Fu sent a letter of submission to Cao Cao and Fu's brother Ben advocated sending hostages while in Imperial Warlords, Rafe De Crespigny makes a note of Sun Quan's courage in making that alliance and sending his army beyond his borders.
In terms of why Liu Bei: Zhou Yu had only 30,000 men under his command, Liu Bei had 20,000 including the navy forces on the Han River. So that was a sizeable reinforcement to face Cao Cao's larger force. Liu Bei was a famed and popular figure at this time while Zhang Fei and Guan Yu were highly regarded warriors, having them as allies added to Sun Quan's prestige (a reason he turned down gilded cage plan later) as well as providing miliatry expirence and known ability for the fight then and to come if the allies won.
Liu Bei also had spent several years in Jing, Liu Qi was the son of it's well regarded but late ruler Biao, his soldiers from Jing whereas Sun Quan's soldiers had been constant enemies and invaders. Such an alliance might have proved useful to ease concerns in Jing for any follow on attack on Cao Cao's new holdings in Jing.
So facing a larger force in something of a gamble by Sun Quan, those 20,000 troops with experienced leaders were a useful supplement to the 30,000 and, though there seems little trust between the allies, the alliance with Liu Bei provided some potential long term use for Sun Quan.
I hope this answer has been somewhat helpful.
Sources aside from the SGZ's aforementioned
Generals of the South by Rafe De Crespigny
Imperial Warlords by Rafe De Crespigny