The problem is more on how you can leave the country you are in without a passport.
Assuming you would be allowed to board the aircraft and fly back to the US, what will happen is that you will have to make an application for admission at a US POE and you have to make a declaration that you are a US Legal Permanent Resident. You will tell the inspector that you lost your passport with the temp I-551. He will ask you more questions on how you acquired your LPR status among other things. He will then send you to Secondary for more inspection to verify your legal status. If everything checks out ok and you are otherwise admissible to the US, you will be offered to file for an I-193 waiver for documentary requirements (you don't have the required entry docs so you you need this waiver). At this time, the fee for an I-193 waiver is $250.00. This is not an application for a new card as opposed to an I-90 application. (Since your actual card has already been ordered you don't qualify for an I-90 application anyway.) It is not a temporary I-551 either and it is only good for that single purpose to reenter the US at that particular time.
After you pay the waiver fee for the I-193, you would be alllowed admission to the US and should be sent on your merry way.