Considering you own other watches that are over 40mm, what is your motivation for going with the 36 vs the standard sized Lange 1 which is 38.5? Its it merely its price and availability at the moment? If you are spending enough to buy a platinum Lange 1, wait and get the one you really want. Taking into account the watch and your wrist, you run the risk of looking down at your wrist and frequently wondering if you should have gotten the 38.5. If this is not a "Keeper" I think you will also find the 36mm a tough size to resell or trade if the time comes for that.
My father has a platinum Lange 1 and the 38.5 is really a wonderful size for a L1. Its modern without being ridiculously over sized, the ratio of the case diameter to its height is simply ideal, and it has a nice weight to it. I think if you go to try on the 36mm, you owe it to yourself to try on a 38.5 on the same day to have a real idea of how you feel about each size.
Wishing you luck with whatever you decide.
My motivation for going with the 36mm is mention spot on by Mr Derek. My purchases mainly from the pre own market and piece like these rarely surfaces and I just can't bare to let it pass. Who know how long it will resurface again. The part where I bolded is also part of the consideration. Its almost the same situation as on of the bro here considering the PAM 392, 42mm vs the 44mm. I think he went with the standard size. But hey, I'll yet have to wear the watch on my wrist to judge for myself. I'll update again when I have the time to try it on.
Thanks once again for your time and opinions.