Not only can you do it post surgery, I actually highly recommend it! The caveat is that you do need to really focus on Protein immediately post surgery because your body needs it to heal.
If you research low carb / high fat diets, you will find the Ketogenic diet, which has been around for a long time used in medical treatments-- not specifically for weight loss. There's a lot of current research suggesting that not only can it help with weight loss/ maintenance, it also is promising as a cancer treatment, Alzheimer's deterrent, and to manage symptoms of ALS and MS . It was originally created to treat children with epilepsy who weren't responding to medications. So, it's a medically sound diet.
I know, sounds too good to be true, right? I'm not making this up! Low carb/ moderate protein/ high fat is actually how you go into ketosis. I lost 106 lbs in the first 8 months or so after surgery, then I stalled until a month ago when I started tracking my net carbs. I have lost 10 lbs in the last month. I'm in the gym 6 days a week, strength training, and running. Because I know what you mean when you say you want to be healthy and strong! I am excited to say that I am truly becoming healthy and strong!!!
We grew up being told that fat is the enemy and the food pyramid we were given said we should have 6 servings of grains a day.....and now we are beginning to see this is wrong, and carbs should be limited! Of course we are going to think "ewww!" when we hear "high fat" but this is referring to the good fats -- the nuts, the avocado, the olive oil.
I started doing it to get myself to goal, but the more I research it the more I see the additional health benefits.
Here's some suggested reading:
http://authoritynutrition.com/10-benefits-of-low-carb-ketogenic-diets/
http://www.ketogenic-diet-resource.com/
and, my favorite:
http://www.ruled.me/guide-keto-diet/
This plan is really working for me. Please discuss it all with your nutritionist (aka your NUT) and figure out what your best approach will be.