How to use same low pass filter for square and sine wave
If you are trying to push the Dds chip to its max frequency, then you do need a sharp cutoff LP filter.  This can get you nice sine waves.  To get square waves, use an analog comparator fed with the sine waves. To get triangles, perhaps use a switched integrator-type circuit, switched with the square waves.  (The triangles are more of a challenge.)
Note: some Dds chips come with a comparator.
A commercial instrument would likely not use a Dds chip, as these are set up for sine waves, but would digitally generate the 3 kinds of waves using 3 different look up tables in the Dds ROM.