Keep in mind that the origin of lagering came from storing the beer in man made caves. At the Urquell brewery, the daddy rabbit of Pilsners, they fermented at cool cavern temperatures (55 or so) and then barreled and stored the beer just down the hall in the exact same cavern until fairly recently. The only difference was they would pack ice, with a drainage canal, through the storage areas.
If you bottle, allow to carb and then lager you should achieve a decent lager. So, a large cooler with a bit of ice would solve the problem. Not too much ice. Just enough added daily to keep your bottles around 40 degrees for a few weeks.
The most important thing with lagers is your diacetyl rest. You must raise the temperature enough to allow the yeast to use up that diacetyl. Otherwise you'll have a very buttery beer. But this rest needs to come while the yeast is still active. I recommend checking your gravity after about a week and once you get to about 70% of your estimated final gravity (maybe about 1.03 or so depending on your OG), move your primary carefully (don't shake it up) to a warmer area until it ferments out.
All that said, lagers are tough. Every off flavor is amplified in lagers because they should come off very clean and crisp. Esters from fermenting too high, diacetyl from not a thorough d-rest, DMS from improper boils (must boil for 90 minutes), and on and on. Not saying to give up on making a lager, but I always recommend starting with more forgiving ales until a brewer becomes confident in the nuances of controlling fermentation.