Depends on your goals. Regardless, high intensity and volume training is the way to go, lifting as heavy as you can with resistance work.
You wouldn't be overtraining on-cycle - more like overREACHING (yes, there is a difference between the two, and many people use the terms interchangeably when they shouldn't).
I still recommend taking at least ONE complete day OFF all training - if not all training, at least one day off from resistance work, to allow for recovery, since your body still needs to recover on-cycle. How many days you lift would depend on what you are used to - for example, if you usually train 5-6 days with weights, then it's fine to continue doing so, but if you usually only do ~3 days, jumping to 5-6 days could be pushing it. Based on that, 4-5 resistance training sessions a week would be my recommendation, depending on what training programme you are following (if you are following one) and how your training is structured.
~Rosie~