It doesn't surprise me that you found Geico's home owner's insurance expensive. I had the same experience. Not only was the cost twice as high as the next company I shopped with, but they had a long list of things to "fix" before they would continue my insurance. I got the message loud and clear that they didn't want to insure my place, and were tree-hating A**holes, which sucks because I love Geico and Berkshire Hathaway. I fixed everything on their list but didn't send them the before and after pictures. When they sent me mail saying the were canceling my policy I was well on the way to cheaper insurance with someone who seemed to care.
I had never heard of Lemonade Insurance before. It looks like they've been around for 6 years, and are recently publicly traded. From their wikipedia page, it looks like they kick the insurance back to Loyd's of London for reinsurance. Loyd's is a reputable place. There are a lot of good names as investors in this new insurance startup, but I really didn't like this:
"It uses artificial intelligence and chatbots to process claims and set a world record for processing a claim in 3 seconds."
At least half the time I call customer service, it's because a company's website is broken or unable to fulfill my request, so I nearly always need a live person. Maybe it's different for other people.