No a single-step 2 liter starter won't be enough for your lager. Your 2-step plan in your OP is solid.
Assuming a 5.25 gallon batch, use a 2-step starter with 1.5 liters in each step. Grow the first-step, cool and decant. Add the slurry to the second 1.5 liter step, grow again, cool and...