This is the official webpage where you can find out what you need to enter Canada:
https://www.cic.gc.ca/english/visit/visas.asp
For LPR, it says
Lawful permanent residents of the U.S. must present these documents for all methods of travel to Canada:
a valid passport from their country of nationality (or an equivalent acceptable travel document) and
a valid green card (or equivalent valid proof of status in the United States)
So yes, if you have a valid proof of your LPR status and passport, you can enter Canada through land borders(provided they are open).
For people with advance parole and no LPR status you need a visa. Also every foreigner entering Canada including US citizens needs to be fully vaccinated 14 days prior to traveling to Canada. One must also submit their information through ArriveCAN app before approaching any land border(or air travel).
Visited Canada in December. Found out that most Canadian airports have US pre-clearance facilities meaning if you are traveling by air, you need to go through US passport control/ immigration right at the airport and you get to a domestic terminal on arrival to the US and no need to go through customs in the US.
