Typically when you stream to something, 2 factors will mainly be important:
1.) Transfer speed, how quick can you transfer something to your local network.
2.) Size of the media casted.
So either you need to improve the connection to your Roku, by making sure you get a "direct line" to it without filters or similair and using 5ghz+ networks or you need to use an appliation like "SecondScreen" to lower your resolution of your phone to make sure it streams lower resolution which will require less data to display properly.