Do I need 30% equity to qualify for financing?

[Richard McNeal]

I just got off the phone with a lender who said I won't be able to get (traditional) financing anywhere unless I sell my house.

I have one rental property with about 10% equity. I'm currently living in a property with about 5% equity. I want to buy another property and move in to it. The lender said they couldn't count rental income unless I had 30% equity in each property, and that that's pretty standard from all lenders. 

Is this true? How do I keep both properties and get the third? -- I'm not getting up to 30% on either property any time soon.

Thanks!