The vinyl on LV canvas bags is polyvinyl chloride. PVC becomes brittle over time, caused by exposure to UV, various solvents, heat and cold. A mild soap followed by wiping with distilled water and thorough drying should be good for cleaning these bags. It is also possible to condition vinyl coated canvas. Avoid caustic detergents as well as those containing ammonia. There are special PVC cleaners and conditioners that protect the material and prevent stiffening, cracking and discoloration. I have personally used a specialty plastics cleaner/conditioner called Sea Glow. This stuff is made by a company named Island Girl and is coveted by collectors of custom sneakers among others. It's not easy to get your hands on a bottle of Sea Glow though, as the people producing it like to take long island vacations lasting the better part of the year, during which they don't conduct any business. This is according to announcements on their website!
I'm sure that other options for conditioning vinyl exist, just keep in mind that only products designed to prevent loss of plasticizers, will do the job.