'Lemon Law' covers a lot of ground. In some states, there must be three unsuccessful attempts to repair, the problem must materially impact the performance or use of the vehicle (in most states squeaks and rattles don't qualify for lemon law, for instance) and/or the vehicle must have been removed from service for 30 days in one calendar year due to repairs etc.
In some states, notably Florida, there are different laws. For instance a safety system such as brakes or steering is allowed only one repair attempt before a vehicle is eligible for lemon law. The single attempt can include a 'no problem found' attempt, meaning customer brought it in, complained of a problem, problem could not be duplicated, customer uses this as a basis for lemon law to get rid of a car.
90% of the buybacks I have seen came from poor documentation at writeup time combined with a big ol' case of buyers' remorse. That's why you'll see the words 'customer states' such and such occurred. If you don't put that in the concern, that means you admit the problem exists. Now the district rep has no choice but to buy the car back and then do his damndest to get the service advisor and service manager fired.
For that reason, I wouldn't be overly concerned about a branded or buyback title vehicle which was done for lemon law reasons as long as you know what those problems were. Sometimes that's not even a big problem; I know of a Thunderbird Turbo Coupe which was bought back over a seemingly incurable backfire condition which turned out to be a bad ignition coil. I saw the coil being tested while it was in the shop, it passed every ohm test the techs used.
The one problem I can see with such a vehicle: if you want to sell the car in a few years, the 'branded' title can make it tough to sell. In some states, used cars are subject to lemon law very similar to new cars and yes it can affect a private sale.