That is not quite it. To extend your analogy to Leveraged Buy Out, what they did first is first borrow $25 in the name of the lawnmower from the neighbor. When selling the lawnmower, they then told the neighbor that the new owner is the one that owes the $25 that YOU borrowed.
This would be all great if it was summer and the owner could mow lawns in the neighborhood, but now it's getting into the winter and the new owner is going to have to wait six months before they make any money back. Then it turns out that the neighbor wants their $25 back now but the new owner does not have the cash. So instead the neighbor says that they'll just take the lawnmower.
The former owner that you sold it to for $75 is now out $75 and does not have a lawnmower. Now imagine that all the gears and parts of that lawnmower are people. The neighbor that lent the money decides that they don't really need a lawnmower and decide that only the motor is valuable and can quickly recoup the the $25 loan. They throw away all the other parts (fire the people) and sell the motor.
You (Bain Capital) are $75 richer
Initial Buyer (Small investors): $75 and no lawnmower.
Neighbor (lender): Recouped initial $25 loan and maybe some.
Lawn mower parts (employees): Without a purpose (job)
You see this is not just venture capitalism where you are taking a risk with your own money. In this case, you are not even using a lot of your own money or taking any kind of significant risk in doing so. The main capital at risk is equity in the company that you borrowed against in order to buy it. If you did not saddle the company with so much debt, it would not be so bad. At least you have some more time until your creditors come after you. Now sure people should not have put more investment into the company knowing that it had substantial liabilities, but a lot of time this is not very obvious due to how they structure the debt.