Just last week i got my first LK10 man kill ever.
Being hit/exp capped dose help and SoL will be one of ur major heals some fights u won't need it but like i show in my LK video you will.
I tryed to do the fight many times like you would if u did it as current raid and i keep hitting the enrage timer around 14-18% on my 22try i had a idea to eat the AOE phase 1 and it worked and upped my dps time by a lot. on the 23rd try is when i recorded it and got my first LK solo kill. I had around ilvl462 but im sure u can do it with a bit less in ilvl maybe 450 is the lows u can do it in and not hit the enrage timer.
In the AOE phase with Sol on use HOR so it applys its debuff to adds and lk so they do less melee damage and each hit will heal you a good amount.
Edit: also to add i have soloed almost all of naxx10 i got bored and stuck on the dog fight and never went back but i did solo KT that was a cake walk. I pulled all adds in his room in phase 1 like 3 times for fun.
There is a few fights you may be able to pull off as ret but i was prot in most of my fights.
If you got any questions you want to ask feel free to PM me or reply to the video at my youtube and ask there.
Also using prot with dps gear is not a bad thing as long as u got a decent amount of mastery to make up for the lack of dodge/parry