After microdiscectomy will a spinal tap affect back?

Likely Not. A lumbar microdiscectomy removes a portion of the herniated disc, a spinal tap removes fluid from csf. Unless your surgery was done recently, having a spinal tap done after a discectomy should not be a problem.
Lumbar puncture. A microdiscectomy should not normally affect the ability to a do a spinal tap. The physician also has the option to do a different spinal level from the disectomy.