Lich is an amazing hero. He lacks a stun, but basically has 3 slows. My favorite thing about Lich is all of skills are always useful. I guess his 3rd skill (the one that gives you mana) won't be so useful late game, but it's great because it lets you spam spells for so long until that point where you get too much mana it doesn't even matter.
My favorite items for Lich are Boots of Travel, Blink Dagger and Shiva's. That doesn't mean I get them every game. Depending on the type of team I go against, or if a specific player is doing really well, I'll switch it up. In the case of the team you were playing against, a Ghost Scepter might be a good idea. It's a cheap item which is later meant to build into some agility item (I think), but I'm pretty sure I've never gotten that upgrade. I get the Scepter for bonus HP and the ability to make it so the other team can't use physical attacks on me.
In that game, it looks like you did pretty well. I'm looking at your inventory though, and I don't don't think you have any type of boots in your game. You always want one of the pairs of boots, on every hero in the game. Normally, you don't want to start out the game with them though.
Your goal with just about any hero, is to be able to hold the lane as possible. This is just a general rule. With some heroes (Lich could apply), you want to get boots earlier, and be everywhere on the map, messing lanes up with your team.
I personally dislike farming and love to be everywhere in the game with just about every hero, so my play-style varies from a lot of players. This leads to a lot of idiots getting me killed because they're not used to something unconventional and will just farm. Often a typical loss for me will result in me getting a ton of kills and assists early while some moron farms, and we end up losing because I'm underleveled and they're bad.
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