When you hit a number of offerings in the same level it gives you an artifact.
The number needed is set for the level randomly and i think i read somewhere it can go up to 60 or something.

Lutfisk is so gross.

After any incriment of 30 lutefisk you get an artifact, not sure if larger incriments mean better artifacts though. 
edit: also under any circumstances DO NOT EAT THE LUTEFISK 

Honestly, don't bother with Lutefusking.Well, you can if you want, but I've tithed over 150 and, even then, I haven't ended up with anything worthwhile.

I could go for a lutefisk sandwich with some surtstromming on the side...

...

gag

It seems to be very hard....

Apparently the stuff it can give can be pretty cool but yeah, it takes a lot of chunks and you are likely to get something mediocre. On the other hand it's a pretty good way to keep inventory space clean though.

The trick is to find a lutefisk horadric box and dump there any cheap/useless item you find, usually weak weapons and armor, potions if you are not a mage and lockpicks if you have the burgarly skill.

I hate lutefisk god , I keep giving Lutefisk to him  and nothing happens...

Every Lutefisk tithed increases the chance of you getting an item by 1%, up to a max of 100%. After you get your Lutefisk God item, the bonuses on it are determined by how many Lutefisk you tithed. That is, the more Lutefisk you tith, the better the item you get will end up being. Oh, and yeah, the Lutefisk Horadric Cube totally helps. It's basically like the Diablo 2 Horadric Cube, except everything turns into Lutefisk.

1,100 hits and only 11 responses!
 
Turns out this thread is second and third when searching for "Lutefisk God".

Well the question was answered in the first couple posts so not too much to add.
 
Anyways here is my lutefisk strategy.  Tithe 1 lutefisk at a time (use a smithing item to seperate your lutefisk into individual pieces, first click puts 1 item in the smithing item).  Usually after between 10-20 pieces I'll get a seemingly random quality artifact.  Tithing large amounts of lutefisk at a time haven't given me anything better then the 1 at a time method.

I once tithed 72 Lutefisk until something happened. The artefact was pretty good though.

Also, another good idea for anyone wanting to Lutefisk. The fungal arts skill is handy if you have a Horadric Lutefisk Cube. Instead of using your generated fungus spores, just turn them into Lutefisk. On a side note...who would eat something that is made with Lye....thats just crazy.