Reginald Lannister is a distant relative of the Lannisters, belonging to a cadet branch of House Lannister established on the city of Lannisport. Reginald Lannister fights for Lord Tywin in the War of the Five Kings. However, Tywin has made him an officer in the Westerlands army solely due to his name, and actually views him with contempt. He is married and his wife remains in the family seat of Lannisport.
Reginald is present at a war council held by Lord Tywin inside Harrenhal. Reginald suggests that the Starks have stretched their lines too thin and will struggle to sustain their army with winter imminent. Tywin rejects this notion, saying that the Starks are more capable than they are of coping with cold. The council continues and Tywin chastises his bannermen for waiting for Robb Stark to fail and that he won't unless they make him. He asks how they will stop Robb and Reginald ignores the question to say that they have been working through the night and would benefit from sleep. Tywin says that he believes Reginald would and that because they are cousins he might let Reginald wake from his sleep. He orders Reginald to return to his wife in Lannisport before he decides to send her his head. He adds that Reginald is only an officer because of his birth and otherwise would be scrubbing out pots in the cook's tent.
In the A Song of Ice and Fire novels, there is no character by the name of Reginald Lannister. Among Lord Tywin's bannermen at Harrenhal there's actually no member of either the mainline House Lannister or the cadet branch.