Can you please expand upon how you will go about obtaining the travel document? To be eligible for a PR travel document, you already have to be a permanent resident of Canada.
PR Travel Document can only be applied by an individual who has already as a landed Permanent Resident or completed such process internally in Canada. However, PR Travel Document can only be applied at a visa office outside Canada. You would be unable to get the travel document endorsement on your passport internally in Canada.
However, when in Lebanon, you will be able to apply for a PR Travel Document at a Canada Visa Application Centre in Beirut. This is because the VAC in Beirut does entertain applications for Syrian nationals. It usually takes a week to receive the PR travel document and I would recommend you do this first thing arriving in Lebanon. You will need to provide evidence of your status in Canada, such as a COPR/landing document and submit your passport with this application. The PR travel document is then received as a visa endorsement sticker on your passport pages.
If you are application is still 'in process', I am not sure you will be able to apply for a PRTD to return to Canada as you have not stated that you have received a PR visa endorsement on your passport, or completed a landing procedure to be considered a PR.
However, I am unsure if refugees are subject to the same passport control as ordinary residents are.
In any case, I will not recommend you travel outside Canada unless your status has been confirmed.
