For living donors, not really. We just performed a spouse transplant between 71 year olds and they have done well. The key point is physiological age, the recipient's need for kidney mass, and the donor's residual kidney function. If there is enough to share and it's in good shape, then donation is good. There should be no difference in either renal function or outcomes if both are performed well.
Some surgeons do remove the right kidney by the lap technique.
We do not recommend that approach. Also it depends if you have been pre-exposed to human antigen and if you have developed antibodies to human antigen. If you have developed these antibodies to human antigen, you will be harder to find a kidney that your body will accept. The incredible wait for organs, especially kidneys, is why we encourage everyone to consider donating your organs and tissues when you die. For some a great deal longer and for some a little shorter, but in reality too long for everyone.