Games went with serve until the 7th game of the second set when Pavic was broken and Butorac and Lipsky were able to hold their next service games to close out the match.
Venus cut a disconsolate figure afterwards.
"I didn't play well enough and am very disappointed, but it's over now so on to the next one."
Venus and Pavic have won three titles on the ATP World Tour this year in Auckland, Montpellier and Marseille, while they were runner up in Nice just prior to the French Open.
The pair now turn their attention to the grass court season where they will play in the Netherlands, Germany, and Nottingham before Wimbledon.
Kiwi Marcus Daniell and his American partner Brian Baker are in action on day four against Marcos Baghdatis and Dimitry Tursinov, scheduled to be the second match on court 5.
The third Kiwi Artem Sitak won't start his campaign until Thursday night New Zealand time.
Matt Brown is at the French Open thanks to Emirates Airline