What's wrong with just "England"? Moreso because lions are not native to the UK, so I can't see why the name was chosen at all. Except I suppose "The Rabbits" or "The Squirrels" or "The Muntjacs" isn't as impressive :)
They were chosen as they are our national animal, they wear the three lions on their shirts and also embody the kind of attitude you want a football team to have - strength, speed, power, agility, working as a team and and having a strong work ethic to support each other ... why would you want a team to be referred to as a prey animal rather than a top predator?
As for why not just call them England ... what happens when, as in 2012 when the Lionesses name really took off, you have both male and female teams playing in games in the same competition at the same time and you need a way to differentiate... Nobody is going to keep saying "England men" or "England women" they're going to default to "England" and "England women" because for many the default is still that football = men. By claiming the Lioness name and using it even when the men's team don't use the Lions then they are giving themselves an indelible identity that can't be confused for the men.
If I say "I think the England team are brilliant" then I could be refering to either team but if I say "I think the Lionesses are brilliant" then there is no way anyone could mistake my praise for the women's team as being intended for the men.
I dont like it as Lionesses is a subset of Lion
It's not our fault that English defaults to the male term though ... Other languages have gendered language from the off so you know whether you're discussing male or female players just from the words without the qualifiers of male/female - eg in Spanish "player" will be gendered whether you're talking about a male player jugador or a female player jugadora so you don't need to qualify it.
If we referred to them as the Lions then people would complain we were referring to the women's team by the male animal term and erasing the women's identity - why use a male term for a female team when there is a specific word for a female lion they could keep using?