Circuit power issues causing LCD to change brightness when motor operates
Add 100nF ceramic caps in parallel to every IC power pin pair close to the IC. This is standard practice.
Add a 100-470uF cap to the motor's power supply closest to the motor and motor circuitry.
Don't power the motor through a regulator if you don't have to. The L293D can handle up to 36V and your motor is not that picky. You gave no specs for your motor but if it runs off 5V it will be fine up to at least 7V.