Are you Canadian? If yes, due the leniency with which they tend to treat Canadians, and the data sharing between Canada and the US, you may be able to enter the US with just your Canadian passport, especially if you have used the same passport before to enter the US with a green card. Upon swiping the passport they'll know you are an LPR. Make sure to have the police report with you, and remind them that you are a permanent resident so they don't accidentally admit you as a visitor.
But you should only attempt this at a land border, or at an airport where they do the immigration screening in Canada. That way if they refuse entry you can simply turn around and leave, and then look about getting the transportation letter from the consulate.
Did you lose the green card in Canada, or outside Canada?