What type of lubricant/grease is most suitable for brake and shift cables? I bought this lube some time back when I cleaned the bearings in my rear wheel:



Now I am replacing all the cables on my bike and the instructions say to use white lithium grease. While I was at the bike shop yesterday, I asked the guy if the above ParkTool grease would suffice and he said it would. However, someone online said that this grease would not work as it would introduce friction within the cable housing.

So what is the correct answer? If I already put that lube on my cables, should I clean it off (if that's even possible) and apply the proper grease?

Edit: For anyone wondering, here's the cable kit I bought:

https://www.amazon.com/gp/product/B00L8NDVD6



And here are the instructions:
A heavy grease may introduce drag between the cable and housing, so a light lithium grease is preferable.

Lubricants can trap dirt and grit, meaning a greased cable would work better than a dry cable initially, but soon become contaminated such that the greased cable is worse.

Using a teflon-coated cable will avoid the need for lubrication and prevent water from being in contact with the steel strands.