How to play Lich in lane.

Play support and play like denying your own creeps is more important than last hits. Deny and sacrifice to stunt your opponents farm massively.

Try to not use sacrifice when the enemy are within XP range. Drop back to pick up the creep wave as sac comes of cooldown.

Harrass with frost blast as often as you can, target the same person as your lane partner, either harass the support away together and maybe get a kill or focus on the carry to limit their farm even more.

The situational items give you options for escape, magic resistance, ridiculous amounts of damage, (refresher orb+sceptre+chain frost anyone?), or armour and more slow for your enemies. You can be ready for any contingency.

Getting a drum instead of the mek is good if anyone else on your team goes the mekansm route. Force staff is a brilliant second item.

Try to hit the chain frost when there are no creeps or illusions around the fight, remember the first hit grants a mini stun, but they all slow attack and movement speed...as well as do a LOT of damage.

Use armour on everyone, attack speed slow and movement slow for any enemies that attack is very useful, nevermind the extra armour.

Buy wards, lots of wards.