I was under the mistaken impression this was new work, and you had not previously mentioned 3 way switches for the lights. Given that, the device I had in mind to switch both feeders and avoid the relay will not work. You can certainly find a suitable contactor with a 120V coil. You will just need to pick up your control voltage from the leg that feeds the lights, and figure out where to put all this stuff.
As far as NEC is concerned, it's just an outlet. It is not required to be dedicated, so it should be no issue that it is tied to other loads. There is also no prohibition against 20A lighting circuits, nor mixing lighting and receptacles (though some mistakenly believe so).
ETA: Make sure you take the control voltage back to the neutral for the lighting circuit.