I love games like that.
There was one game where I was Cho top against a Maokai. We tried fighting each other for the first few levels, but it never got us anywhere. Even jungler intervention only resulted in a temporary retreat or a blown Summoner spell at best/worst. We started joking around about our inability to damage the other, and eventually decided to declare peace in top lane.
We also agreed to get the same builds, since we were both going tanky-AP. We recalled at the same time, got RoA together, then went back to lane and had a dance party. After a while, we went back again, and got SV, Sunfire, and Randuin's.
The laning phase was hilarious, but my team -who had been really chill, and was even joining in on some of top lane's shenanigans- eventually started losing badly. The enemy jungler, Vi, was really good and was wrecking my team. When mid inhib fell, things got serious, and Mao and I both came down to help our respective teams.
In the end, my team lost, but it was still the funniest game I've ever played, and the Mao and I added each other as friends after.