I'd say this is antique -- Edwardian or maybe earlier. I bet Jonathan could pinpoint the exact year. He knows this sort of stuff very well.
Lord & Taylor was a nice (not super-fine like Bergdorf-Goodman, but upper mid range, somewhere between Macy's and Bonwit-Teller) department store. Shopped there all my life. They've always had clothing labeled this way (with only their store brand label, no other manufacturer name -- I probably have some modern stuff in my closet right now). They had in-house designers, as most of the better department stores did, and produced their own brand.
I've never seen anything made of mole (despite my mom being a fur model and my uncle being a furrier). Perhaps it's a name for something else (e.g. "Hudson Seal" is actually muskrat. If something WERE made of mole, it would take a whole lot of moles to make a garment, that's for sure. And if you ever saw a mole with a pelt as large as these, I'd suggest you run! ; )
This does look a like sheared beaver, but perhaps slightly shorter than usual. Photos without a flash would be helpful. Sheared beaver feels heavenly, and was popular in the 1st 1/3 of the 20th century -- my grandmother had a coat I loved to hug). It was not an expensive fur, as furs go, and was accessible to many middle class women (similar to raccoon in the 50s -- oops typo, meant 20s (ljmd) -- for college men). Does the coat feel like very long velvet? Dense and thick and smooth when you brush your hand across it (as opposed to silky and "looser," like rabbit or chinchilla, or dense and sleek like lamb. Does it have longer outer hairs and a dense undercoat near the skin?