The logistical answers are very good, but in terms of what actually happens on the battlefield:
Horses are faster than lion people
On a large enough plain, the existence of well-trained horse archers on one side of the battle but no horses on the other is almost enough to guarantee victory. If they can't be reached, they are free to take potshots at their enemies with relative impunity. They outrange their enemies, because you can shoot farther if you're charging at your target. If there's no easy way for the lions to entrap the horse archers, they can kite them around the battlefield until they get tired and go home. It should be noted, though, that horses will tire faster than lionfolk - bipedal movement is much more efficient.
Avoid breaking lines at all costs
The lion's ideal situation is a chaotic brawl without a clear direction of attack or defense. At that point, it's a few thousand one-on-one fights with a clear advantage on the lion's part.
Normally, the go-to would be shield walls here. But if lions can throw a man, they can also rip him out of a formation, so a traditional shield wall won't do here. Additionally, male lions can probably vault over the frontlines, which would be very bad.
Instead, go with polearms. Very long polearms that mean that by the time the lions can touch the frontline, they have to deal with minimum three layers of soldiers stabbing at them, plus whatever archers are available. 358
The soldiers must be trained to advance forward when the guy in front of them dies, or the line will break.
Adapt equipment
Certain things which make sense when fighting humans don't make sense here. Shields are the big one - a standard shield could be grabbed by a lion, breaking your wrist or throwing you around. An alternative might be a buckler or a hefty gauntlet - a small shield that doesn't provide much surface to grab but still gives you a surface to bock an edged weapon with (block meaning redirect in this case). Alternatively, ditch the shield and use a big heavy iron fence - small humans will have an easier time making use of the gaps in the fence, and it can be made spiky so they won't have an easy time climbing or tearing it down. Or go the simple route and put spikes on the shields.
Every melee weapon used has to be big: daggers and short swords won't reach anything important.
Against the gigantic male lions, consider using a heavy weapon like a hammer to smash their feet. Broken foot bones are as good as dead - that soldier is out of the battle. Once you hit them, drop the hammer and run, or you aren't getting away.
Bear traps/caltrops: the nature of this battle means that humans will retreat and lions will advance, the humans should take advantage of that. Bear traps are free kills (or disablings - even if the trap is removed, that lion can't get to the frontline). Caltrops, nets, and obstacles slow down the lions which means that your archers can get more shots off. 358