Drow Ranger: The Hard Carry

Minor issue with your skill build, you've got 5 levels of Frost Arrows & only 2 of Marksmanship.
Level 12 should go into Silence & level 16 into Marksmanship.
Also I assume the Magic Stick in the early game items is meant to be a Magic Wand to make use of the 2 Iron Branches you buy with your starting gold.
Other than that, pretty solid build & I like the way you've listed items in purchase order including intermediate items rather than just complete recipes as it's much easier to learn for new players this way.

Manta is a great option I agree. It helps you carry harder and gives you a chance to escape. Lothars (or shadow blade for non-dota 1 players) is good for the fact that you can escape easier. Illusions are nice, but Lothars is more of a gaurenteed escape. Especially if they don't have a gem or wards, which is fairly common. If for example your in a team fight, and the one with the gem dies, or you fight away from wards, the invis will save your life, wheras the illusions have a lesser chance to do so imo.

Also in most cases buying a gem will set a hero back, also they will have to invest in more wards.

I think the choice between manta and lotahrs comes down to the level your opponants and personal preference. Personally, ive been saved more often by a lothars cloak than i have a manta.

That being said, build for your situation:)

Edit: also even if they can see you, the move speed from cloaking lotahrs may be enough to save you

Exactly how I drow when I wanna play hard, except just go to manta and skip loathars. Manta is great since illusions benefit only from stat gain like agility from your ult. Manta into butter will carry harder and faster and is less counterable than going for loathars. Always depends on the situation though.