application.conf

db.default.driver=org.sqlite.JDBC
db.default.url="jdbc:sqlite:/absolute/path/to/sqlite/file.sqlite"

build.sbt

name := "app-name"

version := "1.0-SNAPSHOT"

libraryDependencies ++= Seq(
  javaJdbc,
  javaEbean,
  cache,
  "org.xerial" % "sqlite-jdbc" % "3.8.0-SNAPSHOT"
)     

resolvers += "SQLite-JDBC Repository" at "https://oss.sonatype.org/content/repositories/snapshots" 

play.Project.playJavaSettings

DB Evolutions

Add support for db evolutions:

Download the sqlite-dialect from here: https://github.com/gwenn/sqlite-dialect
Compile it to a jar file.
Add the jar file the app/lib folder.