I would say many lenders will deal with the revocable trust because they'll see it as a tax vehicle and not really as a form of ownership. You should expect to provide a full copy of the trust. You should be prepared to sign the promissory note both as an individual and as trustee.
Realize that many lenders may not be familiar with trusts and therefore won't want to deal with it so you may have reduced availability of mortgage products.
I've never been involved in a mortgage for property in an irrevocable trust. I would presume that you could mortgage the property so long as the trust document allows, but there may be mortgage underwriting restrictions I am not aware of.
Shop around. I guess, is really the best advice.