What problems do you have with Lich? I play him a lot and like his style.
Some of the things I do:
Use sacrifice everytime it's off cooldown. First creepwave spawns, use it on the ranged creep before it even gets to the fight. If you don't need the mana, eat the ranged creep. It denies more money from the enemy.
Max frost bite as early as you can and use it as often as you can, especially on squishy heroes. You can get a good kill or two early on with some help from your lane mate/s.
For skill build, I alternate frost bite and sacrifice, sometimes putting a point in the shield (never have it on autocast!) at level 5 if there are lots of melee heroes. Get your ult everytime you can. Autocast is kinda neat, but I've found that it activates at inopportune times. Running away from the enemy? Great, lets stop and autocast a shield!
For ulting, try to get it when the enemy team is grouped up. With the buff of 10 bounces, it can almost be fire and forget. It helps if there are fewer creeps so that it'll only hit the heroes. Even better if there are only 2 or 3 heroes together. Guaranteed kill.
Starting item build: courier, tangoes, salve, ring of protection (for tranquils) gg branches. Then I go tranquils, wards, wards, senties, wards, headdress, wards.... and if I don't die too often, finish mek and maybe agh's. I usually end up playing Lich as a hard support putting wards all over the map. You won't believe how much more farm you can get (via assists) going ganking because you can see the carry farming alone in the enemy jungle.
Hope this helps. I'd be more than happy to play a game with you if you like.