For your 500m² lawn, the MAMMOTION YUKA Mini 800 would actually be a very sensible and capable choice. While you mentioned an interest in LiDAR, that technology is most effective in complex gardens with numerous obstacles to use as reference points for positioning. Since you only have one large Ash tree and a relatively open, flat lawn, the standard RTK-GNSS and Vision system on the 800 model should handle the navigation well.

However, it is worth noting that the YUKA Mini 1000 is currently on offer for £999 (a £200 saving), which brings it very close to the 800's price point while giving you that extra LiDAR peace of mind.

If perfect edges are your absolute priority, you could push for the LUBA Mini 2 with its additional side cutting disk, though it isn't on offer at the moment and its AWD power would be wasted on your gentle slope. For a first-time owner with your specific lawn layout, the YUKA 800 or the discounted 1000 are the best value options.

You can find more information and check current pricing via the links below (affiliate links at no extra cost to you):

YUKA Mini 2 https://uk.mammotion.com/products/yuka-mini-2-1000-robot-lawn-mower?ref=kd2jxen4

LUBA Mini 2 https://uk.mammotion.com/products/luba-mini-2-awd-1500-robot-lawn-mower?ref=kd2jxen4

Let me know if you have any other questions, Mark