Realistically, no-one is going to point this kind of stuff out for you! Lyme Park is very anti-cycling at the best of times (except when being paid large sums of money by the organisers of the Cheshire Cobbled Classic to allow their Sportive to start from there…)
Explore on foot – you’ll soon find the signs of bike use, work out the routes and then you can get in, ride it and get out before you’re noticed. Trying to explore it on a bike in the first place will lead to you riding round in circles, getting lost, pushing up hills and being spotted by the rangers…
You might find some “assistance” on Strava if you run a segment search. Maybe…