There's quite a bit of history to the stretch of the West Yorkshire Cycle Route in that screen shot from the new park-and-ride at one end to the new site of Leeds Grammar School at the other.
The bit being queried here runs near Eccup Reservoir which used to belong to Leeds City Council when the WYCR was devised by the West Yorkshire County Council just as it was being abolished. In those days, municipal waterboards tended to ban any public access to their land so there was a very nice but private road just where it was ideal for the cycle route. This meant that in theory at least, the route took to the fields, for want of a better expression. That was a bit academic anyway, because those responsible for the route didn't want to encourage inexperienced riders onto the roads so it received little publicity and discreet signage which only covered anti-clockwise.
In the heady days of the Notional Cycling Strategy, some of us persuaded the five local authorities to sign the route properly in both directions and to publicise it: that resulted in a rather natty map based on the OS.
By then, water had been privatised and Yorkshire Water took a different line on public access. I've tried unsuccessfully to cut a long story short but I'll guess that ownership of that stretch of lovely cycling road is involved here.
"Notional Cycling Strategy" - lovely. Whether it's intended or not, an excellent misspelling (respelling?).
That stretch over the dam of Eccup Reservoir, and the roads towards Eccup etc. are almost ideal cycling routes. Though I noticed at the start of lockdown there was an increase in motor traffic. A couple of lads in a snazzy beamer were clearly lost at one point near the YW plant. I suspect that some drivers were using those roads as a way of evading police and/or social distancing rules. The road down from Harrogate Road to the reservoir is one of the few places I actually dare to go faster than 25 mph. The other day I got the "what do you think you're doing" hands in the air thing from a motorist coming the other way. If I could be bothered I would have asked him what job he had at Yorkshire Water, as there's a sign clearly forbidding unauthorised traffic. There are a few temporary barriers around the place there. I wish YW would raise them occasionally, to get drivers out of the habit of using that route to cut through, given that it's not public highway, as far as I can tell.
The section of WYCR immediately to the east of Harrogate Road is one of those stretches that somebody on a thin tyred road bike, or a fully loaded tourer, might not consider suitable. Though maybe it's up to me and some other Leeds cyclists to get out and clean it. Another problem is that if you're riding west, crossing Harrogate Road at that point is too dangerous now. These days I'll go west across Harrogate Road on the WYCR, but not east. Traffic is too fast, and sight-lines too poor. If a cyclist decided to cycle the WYCR, and didn't know that particular stretch of road, they'd be at risk crossing it westwards.