Shouldn't be a problem
Shouldn't be a problem. It's not like because you get a new computer the old one stops working. Keep the old Mini around for those few programs you can't upgrade or run on Lion, but then just move all other activities to the new laptop. Worst case scenario you can't import anything from the Mini and make a fresh start with the new laptop.
As for Lion's stability, it's as good, or better, than Tiger. IMO, I'm not a fan of the "iOS-ification" that is taking place starting with Lion. I would like to see Apple go in the opposite direction, and really leverage the unique qualities of mobile and fixed (including laptops) platforms, rather than try and race to some kind of lowest common denominator between the two. I'm probably in the minority though.
Anyway, the one major thing you need to know about Lion, and presumably all versions of Mac OS X going forward, is that there's no longer any restore media to come with the system. Instead there's a special recovery system built right into the firmware of the computer that allows you to download the OS again should you need to. Another change I'm not overly pleased with, but not much I can do except to make you aware of it so you don't spend a lot of time hunting around inside the box for it. It's also something to consider if you don't have a broadband Internet connection. It's just one of the assumptions Apple makes about its users now.
One final little tip, is that if you don't already have some basic ethernet cable around, there's no need to pay the extortionist rates most places want to charge. Something like this: http://www.monoprice.com/products/product.asp?c_id=102&cp_id=10208&cs_id=1020806&p_id=2139&seq=1&format=2 will do you just fine, and shouldn't cost you more than probably $5 shipped.