Yes, this can happen, sort of. You would need to have a guaranteed pick from another team for that year or the following year for it to work most easily.
Say the Blazers want to make a trade. They're right on the edge of the lottery, so they protect the pick 1-14, but guarantee it for 2017 of it doesn't convey this year. Then, after that trade is made, they get another offer they can't turn down. So they say "we already traded our pick of its outside the lottery, but you can have it if it's inside the lottery." The other team is willing to take that risk.
Because these two trades could cause the Blazers to trade all their 1st round picks in consecutive drafts, it's not allowable. However, if the Blazers had an unprotected 1st coming to them either in 2016 or 2017, this would mean the Blazers would still have a 1st round pick in one of those two drafts, and could do the series of trades described in the first paragraph.
It's rare if not unheard of that it occurs in the first round, but second round picks get sliced up like this rather commonly.