The main factors that determine a lion's dominance within a pride include age, size, strength, fighting abilities, previous dominance displays, and alliances within the pride. Lions establish their hierarchy through various interactions such as roaring, physical confrontations, and displays of aggression. Older, larger, and more physically powerful lions are usually able to assert their dominance over younger or weaker rivals. Additionally, forming alliances with other lions can also help a lion maintain its position of dominance within the pride.