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I agree that a Blink Dagger isn't a strong choice - if you want an escape, Force Staff is far more useful.

I tend to get the Bracer first, instead of a Magic Wand, because Lich doesn't tend to take much harass (he can give more than he gets), and he doesn't need the mana recovery from the Magic Wand.

You should skill Sacrifice first, sacrifice a creep as they spawn for the first time, so the cooldown will be ticking while the creep wave moves out.

Lich is probably one of the easiest support heroes to play, and Chain Frost can make you very dangerous, while Frost Armor makes you less squishy. Because you tend to be targeted before you can get your Ulty off, going for a Pipe of Insight is a good idea, because of the Cloak component, which gives you some magic resistance.

Don't waste your ultimate when there are tons of enemy creeps with the heroes you are trying to kill - the creeps will take most of the bounces. Also don't use your ultimate against 1 target - just not worth it (no bounces).

If you are going to use your ulty around Rubick, make sure you cast something else, like a Frost Blast, immediately afterwards.

One word: Escapability.

Why phase? I feel it aint useful for lich since he doesnt depend on his attacks to do dmg

Never start with frost blast unless you're going to start a fight pre-spawn (which you really probably shouldn't anyways) You yourself say to use frost blast sparingly until you get sacrifice. Why not utilize level one and get sacrifice right away to help your lane not push?