When a professional installs a tile floor there should be no visible difference in the thickness of grout lines. I'm not sure what a hard measurement of percentage would be, but lets just say you should be within 15%. Thicker grout lines will give you more room for error, which is why I would use the "visible difference" standard.
Also, the level of the tiles should also be consistent. There should not be any sides or corners that are obviously higher than the others. The "bare foot test" is a good (and again, subjective) way to tell if the tiles are level. They should just feel level.
Those first two are pretty basic and even a DIY person should get that mostly right on their first floor. Another mark of a professional job is the overall layout of the floor. Is there a really skinny tile left on the edge of the room that could be avoided? Was a scrap tile cut to fill in behind a vent when they could have just notched a tile? I would be more forgiving on this last category, but it is still grounds for a complaint.
You have a lot of issues here, and you also appear to have grout splotches all over the floor as well which is so basic I didn't even list that as something to look for... You should complain. No installer in their right mind would argue that they did a good job. Even a "customer relationship manager" with no technical experience would see the obvious flaws here.
The only fix is to rip out and redo the floor. Don't worry about how much that costs and how you are being "mean" to make them do the work. You could have done a better job than this. You paid them for a professional level job, and they make enough money (Lowes) that they can afford to eat a job here and there to fix mistakes.