Besides smoking, mine was actually spitting oil out the muffler onto the deck. I honed the cylinder, put in new rings and a new head gasket on. It wasn't too bad of a job to do, and it doesn't smoke any more.
My 30+ year old Honda was smoking right after starting so I asked our local dealer about getting them to do a top end job (Valves & Rings). They said that if it started and ran OK, don't bother. It's still going and smoking a little - Starts on the first pull.
Just gotta remember to check the oil level at each gas fill or more often when they start fogging.
We had an 60's model Briggs 4 hp. in a small rider on the farm in the 1970's that when running hard on a hot day could burn a good 1/8 - 1/4 quart of oil per tank of gas. We just kept topping it off and it ended up outlasting the rest of the mower. I still have the little fogger in my shed. Still started and ran good until a couple years ago I let some gas go bad in it and gummed up the carb also taking out the pump membrane. Figured one day I would rebuild it and use it for something.