Is the race still iusing 1990's Military tech?
The Race was using essentially 1990's military technology against 1942 Earth Military tech. If you have the Lizards arrive in the late 1990's then there military tech is just more of the same and their ships are vulnerable too, since one or more were destroyed by an ICBM attack while in orbit. The Race would not be much help under the circumstances.
If on the other hand the Lizards are using Mid-twenty-first century technology then - after we could have an entertaining debate about what that actually means - we could pit that tech against the ID4 aliens.
There is no way the Lizards are going to allow the other aliens to exterminate the human race, strip mine the planet and move on as is their pattern. The Race want the planet in a fully functional state for the Colonisation Fleet.
Do they try to do this alone and then conquer Earth? Well what else can they do, they have orders to follow and a colonisation fleet already on the way?
What reason would the Lizards have to work with the Tosovites? Do they need the computer virus to win? If so that would give the humans something to bargain with. Bargaining assumes the Race is willing to do that and can find someone to bargain with while the planet is being hammered and their own force is fighting for survival.
Maybe. The answer to a lot of questions about this scenario is "Well, it depends..."