The three lions could well represent the different territories ruled or claimed by the Kings of England. Certainly, before Henry Plantagenet only two were used. As he kept his wife Eleanor under house arrest for 15 years, and she encouraged rebellion against him, the third lion would have been more likely to represent the place she came from (Aquitaine) rather than her.
However, the lion used in Scotland's coat of arms is rampant. England has "gules 3 lions passant guardant in pale or" ' a red background with three gold lions one above the other, the lions are standing with, three paws on the ground, one raised high.
After many changes, the shield of the UK's coat of arms (and thus the Royal Standard) has been unchanged since 1837, so outside Scotland the three lions appear in the first and fourth quarters of the coat of arms, and Scotland in the second. Within Scotland the red lion of Scotland has precedence in 1st and 4th quarters, and England is only in the 2nd quarter.