You really have two options if you want to try to apply.
The first is to obtain a TRV (tourist visa) to Canada, travel to Canada with your mother and then both of you claim asylum when you arrive. You'll of course need to prove your refugee case through evidence, etc. It will take 2-3 years to know if you are accepted or refused and need to leave.
The second is to be recognized as refugees in Lebanon by UNHCR and then be selected for resettlement in Canada. You don't get to chose where you are resettled (i.e. you don't get to pick the country). So if you go with this option, the chances of ending up in Canada are extremely low.
Thank you so much for replying!
The problem is that we are not registered in the UNHCR. And I don’t think we can obtain a tourist visa that easily because we are syrians, and the official at the embassy who will be interviewing us will know what we are trying to do!
I have contacted a lawyer who handles refugee cases in Canada.
He emailed me back saying that he can apply for me and then he will attach my mother’s file to my file when i get accepted, so that the official at canadian embassy determines if my mother is relying on me financially and emotionally!
It’s really frustrating to not have clear vision of what to do!