Giddo,
Most lenders have an LMI policy on LO or No Doc loans, the difference between them though is whether you pay it or they do.
You didnt mention the loan amount? is this under 500K?
If so you should be able to get what you want with no payment of LMI, at a decent Interest rate around 7.24%, but once again it depends on the deal, how long you are intending to keep the property etc? what's the plan with the property etc, as this has a major influence on the type of loan you get, if you pay LMI now and want to sell the property within 3 years, then it may be better of than no LMI and high exit fees....etc
Mitch