I have the x-rite color checker and I've read that I should create profiles for each body/lens combination and some places even say for each lighting condition, though I have to wonder if that last part is necessary. It would seem to me that what the profile does is calculate the sensor's influence on color perception and correct for it, so why the need for multiple lighting setups? Would it make a difference if I used a light source that is a known color temperature (speedlites, for example)?
The lighting situation is far more important than the lens. (Lens colour casts are really very minimal these days.) You can try to use a dual-illuminant profile, but that will not account for the illumination spectrum that's actually present when you're taking a picture; it's just a basis on which to make gross colour temperature adjustments. If you want accurate subject colour, you need to measure how your camera sees known colours under that light. There is more difference between speedlights and tungsten lighting than Kelvin temperature and "tint" can account for.
Of course, that assumes that you want accurate subject colour, and that's not always the case. You are just as likely to want to see the subject colour as it is modified by the light (by say, a higher proportion of warm or cool tones, beyond the mere colour balance aspect). Flattening it out, or normalizing the response, then trying to put the warmth or coolness back in in your post-processing software will not often achieve the same effect.