He was present at the First Battle of Hoover Dam in 2277, and was also stationed at Camp McCarran before he left to be "present at Hoover Dam" according to Radio New Vegas. He meets the Courier in 2281 during the Second Battle of Hoover Dam. Through conversations with a number of non-player characters such as Chief Hanlon at Camp Golf, impressions of the general make him out to be someone who is eager for glory and victory at the expense of the lives under their command as well as unwilling to listen to subordinates that may question his strategies; Boone suggests he owes his command due to him kissing Kimball's ass.
If the Courier sides with the Legion or Mr. House, Lee Oliver shows his dedication to the NCR willing to fight to the death for its honor, but won't throw his men's lives away just for victory. Many in the NCR disparagingly refer to him as General "Wait and see" Oliver, due to the fact that he gives strict orders to hold position, and not to pursue any attackers, namely Caesar's Legion and the Fiends. His ultimate goal is to mass troops at the Dam in order to gain a decisive victory over the Legion - he feels only a total victory in a straight up battle of attrition would eclipse Chief Hanlon's tactical ingenuity and instrumental role in the First Battle of Hoover Dam; a victory frequently credited to Chief Hanlon.
Eureka!: If the Courier sides with the NCR, General Oliver is the one to brief you on your objectives at the beginning of the battle. After the victory Oliver personally congratulates the Courier in the Legate's Camp.
Veni, Vidi, Vici: If the Courier has chosen to aid Caesar, General Oliver becomes the main antagonist. The player character will need to battle their way through his defenses and reach his personal compound within the dam. There, Oliver can be persuaded to surrender. If not, he escapes to his office, being protected by force fields. The Courier will then have to fight their way through to him, eventually cornering him and killing him.
In the independent path, after convincing the General to surrender with the speech check, it is possible to tell Yes Man to throw him off the dam, resulting in a special cut scene showing him ragdoll over the side of the Hoover Dam.
Question on Joshua Sawyer's Formspring: General Oliver doesn't seem to grasp basic military strategy. What real life persons were an inspiration for his character? Would you agree Oliver's the main cause the war is going badly for the NCR?
He's a mishmash of various aggressive, blockheaded military commanders. Generals LeMay and Patton are obvious examples, though completely without the forethought of those two men.