A fixed asset was lost and disposed (written off) of the books two years ago. Recently the asset has been found. Can we put the asset back on the books? If so, do we have to put it on as fully depreciated or can we put it back on at net book value?

Well, I don't think there is any hard and fast rule to follow here but you certainly cannot put it back on the books at Fair market value.

I think you should essentially reverse the entry you did to write it off in the first place. Then calculate any depreciation that would have occurred during this time and book that too. That would be fair and correct because you’re essentially doing what you would have done this whole time if you had not written it off in the first place. Except now you have to record it all in the current period.