Generally no, for 4 reasons.
First, the 'loss' margin much larger for lotteries than insurance.
Lotteries often take 50% or more. Insurance I don't have firm numbers for, but I would expect much closer to 10%.
Second, adverse selection.
You generally know more about your situation than an insurance company does. So for any kind of optional insurance, you can choose to only take it out if you think the odds are in your favour.
The richer you are, the more risks you can afford to take and the more things become optional, so you have even more scope to pick and choose when to take the insurance.
There is no way to improve your odds with a lottery.
Third, declining marginal utility of money.
Bit of a mouthful, but in simple terms it means that the first $1 Million transforms your life in significant, positive ways. Buys you a house, pays off a mortgage, clears your debts, puts your kids through school and college, gives you complete financial peace of mind.
But once you already have 1 Million, the second Million is merely nice. It's going to make a much smaller difference. The third even more so. 4th, 5th, 6th, 10th, 20th, whatever. At a certain point, it stops making much of a difference at all.
The opposite is true of losing money. You lose $10, and it's a minor annoyance. You lose $100 and it hurts. You lose $1,000 and it could cause you actual problems. For something like a half of all Americans, an unexpected $1,000 bill is more than they can afford. Lose $10,000 and you're going to dig yourself into debt for a long time.
Lose $100k and you're probably bankrupt. House gets foreclosed. Family out on the streets. That $100k loss is going to cause you far more misery than a $100k gain could ever be worth to you.
Which brings us to #4, timing.
A lottery win generally comes at a random time. When you don't particularly need the money. So it's nice to have, as discussed, but nothing special.
An insurance payout comes at precisely the time that you most need it. Your house just burnt down and you're staring that $250k loss right in the face? When $250k is the difference between keeping your life going or losing everything. That's when your insurance payout kicks in.
You know, assuming the insurance company pays out in the first place, but that's a separate discussion.
In summary: Insurance takes money from when you don't particularly need it (it is only of average value to you) and repays, say, 90% of it when you desperately need it, and it's worth a hell of a lot more to you.
A lottery does the opposite, it takes money from you when it's of average value, and gives only 50% of it back in one go, in one massive lump sum, when it's going to have diminishing marginal utility.
When you're desperately poor, there are other factors that can make lotteries less-bad of a bet, but that's beyond the scope of this question. When you already have a Million Dollars, they don't apply.