Using something illegally means you run the risk of going to prison. Let's say there's a 1% chance you get caught, the prison sentence is 10 years, and the evil hackers will pay you $20,000 for your bug. Let's also say that you're a mid-career software engineer in the US, and over the next 10 years you expect to make $2M (after taxes).
This means your expected outcome over 10 years is $20,000 + (0.99 * $2M) = $1.98M. With Lastpass's bounty you end up with $2.001M.
With these assumptions, you should be paying Lastpass to find bugs in their software! Of course, if you're not in the US, you probably make a more reasonable salary (read: less), taxes are higher, and the risk of getting caught is lower.