THD requirement for generated sine
This can't be the way to go: If you have an ideal LPF, one-bit DAC is always sufficient. (Hint: Draw the spectrum of a square wave. Draw the pass band of your LPF on top.)

You don't have an ideal LPF; or you might want to produce a range of sine frequencies (not only a single one) spanning more than an octave, so that you can't just use a fixed LPF + 1 bit DAC.

The easy way to calculate THD is realizing that it's a relation between powers. So, you need to know how much "error power" there is in a quantized signal. There's this term quantization noise that captures that – and it's well-known for sinusoidal signals!