Here in California, we have three distinct forms of bicycle infrastructure, being 1) bike lanes (painted adjacent to mainline road traffic), 2) bike paths (physically separated spaces adjacent to a roadway), and 3) bike trails (wholly separate paths, usually along natural features). There’s a fourth category which are “bike routes” but those are just signage and maps, not actual infrastructure.

When you say “cycle lanes”, what exactly do you mean? If it’s the UK use of that term, I think that maps to California’s bike lanes. Here, I do see a fair number of dog walkers in the bike path. Not all of them, but maybe one in every three. As an bike rider, this just means I have to pass them; they’re usually kind enough to be (correctly) walking down the left edge of the road, facing traffic.

Most areas in this state have narrow sidewalks, so to prevent conflicts with other pedestrian, it’s understandable why dog walkers would want to use the street instead. It’s the same why joggers also use the street, since it’s usually a smoother surface where tripping is a non-issue.

For the traffic levels in a suburban area, I don’t really see an issue. In an urban area, it would be a major issue because of the bicycle volume. So I’m not sure there’s a general solution, apart from advising dog walkers to walk while facing traffic, so that the conflict can at least be negotiated safely.