I also agree it should be no problem having 4 in a 120g, and also would get all females.
I don't notice mine needing or requiring a great amount of swimming space at all.
When I got mine they were bagged seperately, and I got one male w/ a harem of females, and one female ended up somewhat mid transition, slightly higher dorsal.
I knew it would be next in line and eventually did turn male, and of course in time that led to fighting.
If I had to do it over again I'd just get all small or medium size females.
Any aggression I see among lyretails is very mild, nothing I would be the least bit concerned about.