A 40gr bullet with a MV of 1255fps (Remington Golden bullet) is doing about 900fps or slightly less at 200 yds. The 140ft/lbs of ME is down to 71 ft/lbs.
Note that, at 200 yds it has HALF the energy it has at the muzzle.
And, according to the chart, from a 50yd zero, drop at 200 yds is 43.1 inches.
So, half the muzzle energy and a drop of over 3 and 3/4 FEET makes the .22 LR a poor choice for shooting anything at 200 yds.
Even IF your rifle will group well at that distance, for shooting animals at 200yds its a really poor choice.
And, I didn't mention wind drift at that range, which could put your shot off the mark by multiple FEET as well.
it is simply not enough energy for that range unless you're shooting paper targets. and the large amount of drop and wind drift will make shooting targets a real challenge.