Old edition of Book of the Lost Tales 2 signed by Adam Tolkien, with long dedication

If you truly want to sell, an item like this would best be put up for auction. It would go for the amount people are willing to pay which should be good amount if it’s a 1st edition

As with all books that are signed, good condition and provenance for the signature will increase the value. If you want a true valuation from members it would be good to provide photos of the item.

I’m not sure Adam Tolkien’s signature increases the value a whole lot, (perhaps if someone is specifically looking) but others might disagree with me.

I think it depends on which book you have Adam's signature.
I have several books signed by Adam, as I met him several times, for example, he signed for me the catalog of the BNF exhibition (as he held a conference there). He signed a copy Children of Hurin, and his signature is significant in this one as he assisted his father, as we can read in Christopher's preface.
I also have a copy of Peoples of Middle Earth, signed my him and his mother Baillie, to whom the book is dedicated.
Adam also translated in french the Book of lost tales, part 1 and 2, so having his sig in these two is very valuable, as grandson of the author and translator.
In general, Adam is reluctant to sign a book he's not worked for.
But anyway, he's such a nice person, and I'm grateful to have met him, and hope to see him again.