I'm assuming you're not throwing a full-roller.
You need to determine which hole your ball track is catching to determine the proper fix. With your grip facing you, fingers over thumb, place a piece of thumb-hole tape just left of the top left finger and just left of the thumb hole. Throw a few shots and you'll know pretty quick if its your finger or thumb.
If you're throwing an LT-48 from the 80's, it will always go straight regardless of how you throw it. Urethane is hopeless on synthetic lanes unless you're from Sweden.
Getting your ball off the finger/thumb is simply a timing issue which requires you allow your ball to tilt more before you deliver it.
To get more tilt without dropping it, requires split second timing and a firm wrist. A wrist brace can help.
Your ball needs to come off your thumb just before it arrives at the bottom of your swing. If you wait until the ball is passed it's flat spot at the bottom, it's too late.
As the ball leaves your thumb it will begin to tilt. The more tilt before your fingers come out, the more axis tilt the shot will have. More axis tilt will move your ball track away from both the fingers and the thumb.
However, if you track away from your fingers and still catch the thumb or away from the thumb but still catch the fingers, then you'll need to look at the way your ball was drilled.