A great analysis but I have reasons to believe that it's a bit far from accurate, the 1 in 13m chance you have with the lotto is once every week, while the odds for hitting a block which you mentioned is based on a shot every day, so for this to be a bit more accurate you need to multiply the lotto ticket cost by 7, and then if we were to assume that the average lifespan for the miner is 2 years, then you will need to multiply that by 730, so if the ticket price is 2$, you will pay $1,460 to match the number of trials that a miner can have.

I am aware that there are other prize catogires of 3,4,5 matches but I think the prize is too small ot be considered, you also need to keep in mind that when you hit a bitcoin block you keep all the rewards and nobody can share them with you, where in the lotto, you are subject to share the prize with x amunt of people, on the othre hand, playing the lotto means you won't have to pay the power bill, no matiance, no cleaning no dead PSUs or a firmware glitch.

There are many more factors invovled to determine which would be econcmically better, I don't have the time, skills nor the desire to do that in-depth analysis (pehabs someone who does play the lotto and solo mine at the same time can do it) but I do tend to agree that perbaps and most likely playing the lotto is cheaper than solo mining.

With that being said, Solo mining is way more fun!!