I see numerous red flags in your post that all speak to getting a 2nd and a 3rd opinion/estimate.
Run your A/C for quite a while and to see if it cools all the while checking the compressor outside to see if it runs. Not the fan, but the black box at the bottom that will make a sharp and loud whine when it kicks on and runs. Usually when they don't run, the first thing to check is the starter capacitor which can go bad. Without doing an electronic check for a short, etc., a visual check of the capacitor (the large can with wires usually about 1"or2" by 4" or so" wide and maybe 4" to 8" long) will sometimes reveal where the capacitor can has blown out or expanded end or side on it.(He should have caught this though and especially if he replaced a switch (probably the anti-sail switch).
Compressors can go bad but with Lennox you may still be under warranty (I think it is about 10 years or so)(I just had a vcr go bad 7 days after the warranty ran out so go figure). I suggest getting an opinion/estimate from a Lennox dealer.
I am concerned about the entire replacement. Around here I know some will argue over 2.5 and 3 ton in an average size home and some will say you don't want to oversize your unit. You are probably ok with the size you got if it has been working ok in the past for you.
If the coil inside the furnace plenum is ok I wouldn't spend the money to replace it and actually it has no electronics on it. A lot of brands are interchangable like the coil, compressor, capacitors, motors, thermostats, etc (not much left) and you just need to have the right size replacement.
I wouldn't want to say you are being scammed cause maybe he was just giving you options. You unit may be at the end of its warranty, but it could last another 10 or 20 years, you never know. His cheap deal on the side is fishy but maybe it came from a new order that was undersized or just traded in cause they didn't like it(another red flag). It could also be a cheap deal cause they are a cheaper brand unit but you should get a new warranty with it but then again is it a brand new unit or used and if brand new, why does he personally have one? I don't want to accuse, but your Lennox could be the "next" cheap deal on the side being offered to a consumer.
Get more opinions on the repair and size and I would just spend a few hundred bucks replacing the compressor if it is out of warranty.
Post back with the square footage of each floor and where you live.