You can definitely lager in a fridge, no problem. When I lager, I keep the beer at 34 degrees for about 8 weeks, which is easy in a fridge. The issue with lagers is the fermentation temperature- the lager yeasts like to be in the 46-52 degree area (more or less, depending on yeast type, but 50 degrees is about right for all of them). Less than about 45, and they won't ferment so that's why a fridge without a temperature controller won't work for fermentation. Lagers take 2-4 weeks in primary and then the rest of the time is secondary/lagering time.
I primary for about 2 weeks at 50 degrees, and then taste for diacetyl. If I detect diacetyl when fermentation is about 75% finished, then I do the diacetyl rest for 24-48 hours in the low-mid 60s. If I don't detect diacetyl (and I usually don't need a d-rest, since I pitch cold and many yeasts dont' produce much diacetyl), then I rack to secondary and begin lowering the temperature 5 degrees per day until I am at 34 degrees. Those temperatures are why many people use a fridge or freezer with a temperature controller.
I'm lucky, I guess- my basement is 49 degrees in the winter, so I can do this in my basement and then use a cooler and ice and water (I made a new lid for the cooler, so just the airlock pokes out) to bring down the temperature 5 degrees per day and then lager it for as long as 12 weeks if I want- just by changing the frozen water bottles every few days.
Temperature control is pretty critical with lagers, so many people just go ahead and use the fridge and controller.