I would expect the performance of SQLite for queries against an index to outperform MySQL and PostgreSQL in all cases - because SQLite eliminates the need for network overhead by essentially executing those queries directly as a C function call.
So no matter how optimized MySQL and PostgreSQL are, SQLite will run rings around them for basic SELECT queries.
There's still serialization and deserialization overhead there. I would expect SQLite to win in benchmarks against MySQL or PostgreSQL on a Unix socket for basic "select * from table where id = 5" calls, but I've not done the work to prove it myself.
So no matter how optimized MySQL and PostgreSQL are, SQLite will run rings around them for basic SELECT queries.