Paper filed return has been lost by the IRS, should I e-file the return?

How can you be sure the return is lost and not in the gazillion unopened mails sitting in the containers in their lots?  OK, maybe not gazillion; the latest estimate from the IRS for unopened returns is about 2.5 million but that's still pretty darn close.  Refiling a return may just confuse the IRS when that paper return does get processed.

Did your client send in the return using certified mail or courier?  If so, your client should know at least whether the package had reached the IRS.

When you say you don't have an efile PTIN, I suppose you do have a PTIN (otherwise, you shouldn't have prepared that return in the first place) and you just don't have an EFIN.  Unfortunately, without an EFIN, you won't be able to e-file any return.  Nevertheless, if you anticipate that you would prepare more than 10 returns in a year, it is mandatory for you to e-file unless you meet one of the exceptions.

@itonewbie stated the exact answer.

You should probably start the process to get an EFIN now, as the process takes quite a while. https://www.irs.gov/e-file-providers/become-an-authorized-e-file-provider