I'm with LV for my car, buildings and contents insurances and think they're very good. My dogs are insured with NFU (National Farmer's Union) but that's not because I think the LV Insurance may be poor, but simply because a friend who had made loads of claims on her 2 Cockers recommended NFU to me when William was a puppy.
Looking at the 2 policies offered by LV the expensive one looks to offer lifetime cover,so no age limit for your dog, and £5K per condition during the dog's lifetime. So if your dog had an ongoing condition such as Dry Eye you'd be able to claim year after year until you'd exhausted the £5K. That would apply for each and every condition, so £5K per condition.
£5K is probably plenty enough for most lifetime conditions (William has Dry Eye and his 6 monthly check ups and daily eye ointment tot up to about £200 per year) but I'd be concerned that it might not be enough to cover something really major such as spinal surgery and then follow up therapies, or surgery and chemotherapy for cancer. But it's impossible to predict things like that.