To turn that particular beer into an actual lager, all you need to do is buy a lager yeast (my favourite, and a popular choice, is WLP833). These require quite a bit of work though - a big yeast starter (or lots of vials = $$$), chill to low temps, ferment cold, lager even colder. You could use a dry yeast (Saflager 34/70 is acceptable), but you'll still need at least two packs if you don't make a starter..
My lager ferment schedule is: cool wort to 43F - pitch yeast. Allow a rise to 47F over two days. Keep at 47 until 50% fermentation is complete. Drop temp by 1F per day, until at 38F. Keep at 38F until fermentation is complete. Drop 1F per day to 32F. Lager at 32F until beer is clear and ready to drink.
You can easily just pitch yeast and ferment at 50F for a few weeks, then drop temp to 32F for lagering.
Be aware that both of these methods need a big pitch of healthy yeast - I aim for about 20billion cells per litre for a standard gravity lager.
As you can see, this is nowhere near as straight forward as the standard Mr Beer kit.
As an alternative to the kit, you could also try buying extract and hops. Most brewers would start doing this (or even brewing all-grain) before attempting a lager.