I have a honda hrx217tda walk behind lawnmower.

While mowing the yard after about 45 minutes it started to expel white smoke, getting worse while it ran. It has oil in it and there was no problem the week earlier. Any suggestions?

That happened to me one time and it was because I would tip it over to clean around the blade and oil would leak into the engine and smoke would come out of the muffler.

Yep.
Since its white check the crankcase oil for gas contamination and see if its above the full oil level ( overfilled) .

Usually the white smoke is a sign that the crankcase oil is getting contaminated with gas, that is if the Head Gasket is good. That can be check with a compression check to see if the valves and rings are good.

It could be the carburetor needle valve is letting gas leak into the carburetor and flooding the cylinder(s) when the Engine is sitting in time.

The Gas will seep by the rings and get into the crankcase. The oil is to high and thinned and gets by the rings and into the cylinder when you run the engine. We call this "blow By" This is what usually causes white smoke. Put a piece of paper in front of muffler and see if its spitting fluid, spotting the paper.

The white smoke from a lawn mower is like white smoke form a car except a cars white smoke is usually a bad head gasket and the anti freeze is going through the combustion chamber and out the exhaust. The gas in a mowers crankcase is a liquid and evaporates out its muffler like antifreeze does in a car. .

Like light bulb mentioned. Flipping mower to clean then white smoke. Yours is getting worse because of oil thinning out.