Many websites have different views on feeding bunnies lettuce, due to this I have not given mine any yet. 

I was just wondering why certain types of lettuce are ok to give them and others are a definite no?

No Iceberg. Any other kind of lettuce is ok, in small amounts. It has low nutritional value but is good for hydrating your bun due to the high water content. I'd give little amounts often, it's good as you know your bun is not dehydrated!

I have read not to feed bunny any lettuce ... I like to know about Mizuna? Can you feed bunny that? ... Sorry I do not know the English name for it.

Lettuce is recommended and should be fed. Mizuna is fine to feed your rabbits Murasaki.

Iceberg is not recommended because it is conventionally grown and the outer leaves have a higher degree of pesticide residue according to Dana Krempels.

If you look under the Bunny Info section (green banner above) under the Diet section, you'll find great advice on exactly what foods are good for your bunny. Definitely begin to introduce greens slowly, like 2 a week or every couple of weeks. Only iceberg is not good, as it doesn't add any nutrition to the bunny's diet at all, and risks pesticides.

Here is the list from that section that is recommended fresh foods:

http://www.binkybunny.com/BUNNYINFO...fault.aspx

Romaine and green leaf are healthy and delicious for bunnies.

I am pretty sure almost all lettuces are ok but iceburg for the reason that Sarita posted. Spring Mix is a staple at my house-its Baby romaine, oak leaf, endive and radicchio lettuces.