Is it necessary to have lab results done by a primary physician or can the test be done at labcorp/quest diagnostics ?

If PSs have a preference, they will specify the lab.  Otherwise, either the PCP's lab or labcorp/quest can be used to perform the labs requested by your PS.Most surgeons will do some blood work prior to surgery, but some surgeons do not.  It is always best to ask these questions of your chosen surgeon as recommendations may be different.
The surgeon you select should know everything about your past medical and surgical history and be able to make a determination about what labs should be ordered, the need for EKG, the need for medical clearance, the need for anticoagulation, the appropriateness of the surgical intervention based upon the risk factors and current physique, etc.

We generally request medical clearance before any procedure done in general anesthesia. This is in particular important if surgeon did not have chance to see patient multiple times before surgery and hes no detailed knowledge about medical condition(s) that may jeopardize safety of surgery. You can do your labs in any lab but for medical clearance it is best to be done by your primary care physician (internist, family medicine) if you have one. If you do not have your PCP it is best to do it in medical office recommended by your friend, practice near you home or one recommended by surgery center staff. Good luck.