You can sue anybody for any thing. Fill out the papers and pay the fee, and the process starts.
The real question is will the suit be dismissed quickly or will it continue? What *exactly* would you sue the lottery for? "Not being able to generate every possible combination" isn't a cause of action in itself. OTOH, if the lottery claims that the RNG generates random combinations and it doesn't* there might be a cause of action. If they know it can't generate them all they may be committing fraud if the court believes they claimed it was possible. If they don't know, or if any given RNG is malfunctioning they might be found negligent.
The next question is what damage you suffered and how much they owe you as compensation, and that's the problematic part. Whatever the deal is with the RNG, when it spits out the ticket there is no winning number for it to match. Once the winning numbers are selected there's a chance it will match the numbers on your ticket regardless of how few of the possible combinations the RNG could have given you. You'll never be able to prove that you would have won something if the RNG could have generated combinations from a larger pool, so your maximum loss is limited to the cost of the ticket(s) you bought.
About the only realistic possibility I see would be if you shared a parimutuel prize with an unexpectedly large number of winners because a significant percentage of the RNG's only generated a limited set of the possible combinations. In that case probability would demonstrate the amount of the damage. You'd still have to prove that the lottery had failed to meet some obligation to you. In the past, NY advertised benefits of playing QP's. I believe one of th eclaimed benefits was that the comb9inations played would be more random (no concentration of birthday numbers, for example) and that jackpots would be less likely to be shared. If they made that promise and failed to deliver you might have a good case. Note that you would have to prove the RNGs were defective, not just that there were more winners than suggested by probability.
*Note that the numbers aren't ever truly random, in that they are limited to those that are used in the game. Obviously the RNG shouldn't randomly spit out numbers that aren't in the matrix. If an RNG was programmed so that it could only generate 20% of the possible combiantions it could still generate randomly from within that 20%. What is an advertiser actually promising you if they simply say you'll get a combination that is random?