Thanks for asking the question. I have not heard of this company until today, so it was fun taking a look at this.
I don't think it is P2P.
It is directly sold, similar to brands like Geico and Ameriprise, where there are no local or third-party agents to serve you. So commissions aren't embedded into your premium.
However, they could still be charging you more than another insurance provider. You would need to get a quote and compare to find out.
Since they appear to be a small company, they would package their policies to a re-insurer, who assumes the most, if not all, of the risk.
They brand themselves as a social enterprise, so profits are supposedly donated to charity. So, it appeals to people who think they are supporting a good cause. As always, it is important to deep dive and see how much of their profits actually go to the non-profits you care about.
Competitive edge is generally defined as:
Are they better? Easy-to-use UI might be good. But how is the coverage in their policies? How's the claims process? Do you value donations to charity?
Are they faster? Is it easy to purchase? Do they respond to claims quickly?
Are they cheaper? Get a quote and find out.
Usually if it meets 2 of the 3 factors above, then the product/service is considered competitive, ideally 3 out of 3. I am quite satisfied with my insurance company right now, so I am not going to try switching, but you can give it a try to see if Lemonade is a good fit for you. Have fun!