Hi Jennifer -
When you say you've been approved by two lenders, I assume you mean preapproved? Because they won't actually approve the loan with the life estate attached to the property?
The problem here is that if you were to default on the loan, there's no practical way for the lender to foreclose on the property. They could take ownership, but they couldn't evict the tenant. Which is a situation lenders don't want to deal with.
If you're set on this home, you might check with a real estate attorney to see if there are other options, such as buying out the life tenant's interest in the property. Otherwise, the simplest thing may be to find a different property.