13 to 6.5 in 2 months ? Sorry but I don't believe that one bit.. I have done keto before and I think it's cool to try depending on your goals. Myfitnesspal is a good app to start off with beginning Keto for sure so you can draw a baseline of your total cals and macros..
First week - 10 days are an adjustment phase obviously in the absence of carbs and you will drop a shit load of water weight during that period so don't let it confuse you, obviously losing "weight" means nothing..
There are also a few variations to the Keto diet. At some point you will not be able to lift with the same energy and intensity I dont give a shit what anyone says, but if you lift like a bitch and do moderate LISS you will probably be fine.. What are your goals because I lift very hard and I would certainly go back and change some shit when I did start Keto because although I lost some weight I definitely lost some LBM.