Eric,
I'll leave the math to you, but here is an idea, no idea whether it would work. (You can try the math in LabVIEW, without using a DAQ to see if you can get all three frequency components.)
The simplest mixer just multiplies two signals. Assume we have two sinusoidal signals at frequencies f1 and f2, when we multiply them the possible frequencies are f1 + f2 and f1 - f2; the sum and difference components. This is true if we have pure, ideal sine signals.
Now assume we have two square waves at frequencies f1 and f2. If you multiply them together, once again you get sum and difference components f1 + f2 and f1 - f2; however, the square waves contain all of the ODD harmonics, that is, 3f1, 5f1, 7f1, etc and 3f2, 5f2, 7f2, etc. So now you have sum and difference between all these possible combinations, including 3*f1 + f2. (In your earlier post you used the third harmonic, if you need the even harmonics then this will not work.)
Assume we have a function generator with 4 synchronous outputs, see if NI has one. In LabVIEW I can create the signals I want. For one ouput I put a square wave at f1, for another output I put a square wave at f2, for another output I put f1 times f2. That is I am doing all of the math for these signals. I can electronically filter bandpass the mixer ouput for the frequency I want, (hard to have that narrow of a filter) or I can use a math filter in LabVIEW before outputing to analog out for the frequency I want (probably easier). Now you can have phase synchronous signals at three frequencies. (Try the math in LabVIEW.)
Just saw what Lynn said, who is a lot smarter than me. I may be mistaken here, but the time constant on a lock-in amplifier sets the frequency discrimination; for example a 100ms time constant would give you a 10 Hz frequency discrimination. (Here I am referring to a stand-alone instrument, such as the SRS 844.)
Hope this helps.
Regards,
mcduff