I'll pass along some emailed advice from my buddy, a good and long-time brewer. My first lager (done last weekend) is sitting at 10C right now.
I got my wort to about 55 using a two-step IC cooling method, but it took like an hour and really sucked. By the time I let the trub settle and racked it was back up to 60, an it took my fridge like 5 hours to get it to 53, when I pitched.
Make sure you pitch enough yeast, I had 500 billion cells from a two-step starter for my 1.055 Oktoberfest.
My buddies helpful info below:
What is your typical procedure/ferm schedule for lagers?"
"Chill the wort to about 50F, or as close as you can. Oxygenate and pitch. Hold temp until fermentation starts to slow (a bubble every ~3 sec), then raise to 60-65 for a week. (To be honest, I would probably do a intermediate step @ 55F in between as well. So, maybe 50 for 4-5 days, then ratchet it up to 55 over another 4-5 days, and finally up to 60-65 at the end. But that's just b/c I like to tinker with my temps and I like to imagine my yeast will like me more if I reward them with a little temp bump. I really don't think that middle-bump is at all necessary.)
I've only done 3 lagers in my lifetime, and all of those were on my friend's system in which the wort runs out of the kettle through a counterflow chiller on the way to the fermenter. So I am able to get the wort really close to 50 degrees right into the fermenter. That may not be possible with just an immersion chiller, and certainly not in warmer weather.
Some people say it's okay to pitch lager yeast into warm wort (~60-65F) and then gradually bring it down to fermentation temps (48-52) over the next 6-8 hours, the theory being that the yeast reproduce nice and quickly during the lag phase @ 65F (which is a good thing), but by the time the yeast start actual fermentation and producing esters and flavor compounds, the beer is at the appropriate temp (50F) and so there are no ill-effects flavor-wise. Theoretically that all sounds good, but I think it still makes a small difference in the flavor when you shift the temp on the yeast that much.
So, if I were limited with how cold I could chill my wort in the kettle, I would get it as cold as I can with the immersion chiller, rack to the fermenter, be patient and let the fermentation chamber take my wort down to 55. (I can imagine it taking the rest of the day, or even longer, depending on how far it has to drop.) Then I'd pitch and let it drop on down the rest of the way to fermentation temps (48-52). MY theory being a compromise between the impatient "pitch now" camp and the impractically patient "wait forever if you have to" camp. The only downside to waiting a long time to reach pitching temps is risk of infection. Nothing to joke about for sure... but if you were careful beforehand not to let anything fly into your kettle while the wort is cooling, and if your siphon and fermenter are clean and sanitized, it's also nothing to worry about.
Make sure you pitch more yeast and give 'er a longer dose of O2 than you normally would for an ale. Maybe 60-70 seconds' worth."