Thanks to all for the feedback.

I've continued fiddling with it over the weekend and have found several combinations, along with a different app that seems to give me what I want.

MyMyFitness is a general fitness app that will track cycling workouts and sync info directly to my nutrition app.

So I'm going to end up with some combination that looks like this.

Cycling miles (using MapMyFitness) ==> to Lose It! ==> to Apple Health

While fiddling with it I discovered that Strava will do the same combination.

There are some other options I've figured out. For example, Apple Health will take data directly from numerous apps, including several that I mentioned above, and integrate them in the Apple Health dashboard, but those abut that forces me to use Apple Health each day.

My primary goal is to daily integrate the cycling app with Lose It! but to check Apple Health only occasionally - not the other way around.

Another factor is the online access to my history. All of the MapMy apps offer an excellent online dashboard, but MapMyFitness is the only one of the three that integrates with Lose It!

Strava also has a decent online dashboard and a slate of related apps that is almost overwhelming, but I only need a basic feed.

So I'm thinking I'll land at MapMyFitness for workouts (including cycling), and go with that.

Thanks again to all!