I used to get this all the time, my iPhone would steal my laptops IP address.
Some bloke who thinks he is gods gift to everything told me this was impossible and I was being stupid. I sent him a screenshot of the router admin page, showing both devices listed with the same IP to shut him up. He never replied after that oddly.
To solve it, I changed the lease time to 30 years, so all devices will keep the IP they are assigned. Alternatively you can turn of DCHP and set the IP's to static manually.