Uber has already established a presence out the US in Australia, South America, China, the Middle East and Africa. But Lyft operates globally through partnerships with local ride-hailing services in other countries.
But according to CNBC, Lyft plans to change the nature of those relationships.
Currently, Didi users in the United States are able to book a Lyft car directly through their Didi app without having to download the Lyft app.
But Lyft told CNBC, "Along with our international partners, we are updating how we serve our users traveling abroad. We will now direct them to download the partner's app in the country they are visiting."
As of next week, Didi or Grab users who open their apps in the UW will receive a message prompting them to download Lyft, and vice versa for Lyft users that open their apps in China or Southeast Asia.
It's unclear how users will respond to the change, which essentially asks them to give up valuable screen real estate and storage on their smartphones.
The official line from a Lyft spokesperson is that "this will provide travelers with improved functionality and service in local markets."