What yeast did you use? You are fermenting at lager temperature so hopefully you used a good lager yeast suited for that temp. I usually find slow starts to my lagers if I haven't pitched with saved yeast slurry, even when using a good starter. Make sure your lid / airlock is tight with no leaks, which could look like no activity. Check and recheck. Hopefully your starter was foamy, active and proof of active live yeast culture. If no activity after 48 hours I would repitch using yeast right from the package. I like to pitch lager at about 80f and bring the temp down to 55 F asap, a few hours, gives yeast a jump start and avoids lag time. My last lager, 3 days ago, started within in 6 hours like this using saved yeast slurry.
Splashing and oxygenating cooled wort before pitching is important for lagers as well.