At this time ebooks are not swappable on PBS. If you look in the eReader forum there are some groups that use the sharing function of their eReaders to share with each other (credit use is prohibited), but even though you receive these free, most e-books are not an ownership transfer, but are only a right to use the book for your own reading and they cannot be transferred or sold to someone else.  From the Help Center:

Not allowed:

• Anything that is not a book (this includes calendars, coloring books, blank journals)
• Anything that contains advertising (such as single-issue comic books or comic book digests or magazines)
• Advance Reader Copies* (also known as ARC s, Review Copies or Uncorrected Proofs--these are not the final versions of books)
• CD-ROM books/e-books (books that must be read on a computer)
• Burned copies of audio books
• Xerox or otherwise unoriginal copies of books
• Electronic media of any kind
• Unbound pages
• Music recordings, spoken-word recordings (these can be swapped at SwapaCD)
• leaflets or pamphlets or booklets** without ISBNs (other members complain at spending a credit for these)
• Brochures/Promotional "first chapters" of books - these are not complete books, even if they have an ISBN
• Books that require supplementary non-media materials to be useful (non-media materials cannot be sent by MediaMail, and original non-media materials cannot be expected to be included with a used book)
• Pornography (sex manuals and erotica are allowed, hardcore pornography is not allowed)
• Supplementary media alone (without the book they originally accompanied)
• Audio language courses without accompanying bound book.  (if audio tapes/CDs ARE accompanied by a book they are considered a bound book with accompanying media, and swap for 1 credit. They are not "audio books," which are books read aloud by a narrator.)

I'm not sure of all the legal details, but as a general guideline it's illegal to transfer ownership of e-books.  Regardless of whether you paid for them or not, transferring ownership is the bottom line issue.

Unfamiliar with Librarything, but regarding giveaways and such...the author and/or publisher may give away a certain number of copies for promotional use, but that does not in itself allow you to share or give these copies to others.  Probably your best information would be from the individual publishers, check their websites and see if they have information posted on this subject. 

Are you talking about books that you got from Early Readers on Librarything?  I'm pretty sure those are supposed to be non-transferrable since they are promotional type offerings. 

Without specific details I can't say for sure though.  Denise's suggestion to check with individual publishers is a good one. 

TPTB here have given us our own thread.  Please check out eBook readers
 There are lots of people there that will help you figure this out.  We have also formed a Yahoo group to trade ebooks.  Come join us!