It is technically open to members only, with a £5/y subscription. See: https://www.ouwg.org.uk/visiting-boundary-brook-nature-park/

Sure. I ended up with the Broad-Magdalen corner which seemed more central from a geographic point of view, but Carfax makes perfect sense. Go ahead!

Thanks, you're probably right. OS OpenData has it as "Lords's" however. I can also find a couple of uses in published work both for "Lord's" and for "Lords". I will double-check the local sign next time I'm there.