In Connecticut, if my name and my fathers name are on the deed to my fathers home, but only my fathers name is on the mortgage, does the house legally go to me upon his death. By the way he left no will. ( I realize the mortgage will have to still be paid if there was no mortgage insurance to pay it off upon his death.)

Depends on how the deed is worded. If you have right of survivorship then you get the property. With other forms of ownership his share goes into his estate for distribution to his heirs.

The mortgage lender will still have a lien on the property.

Does the deed state tenants in common or joint tenants? The latter gives you right of survivorship.