Something that is more lyrical requires a slower, shallow vibrato. Know the rules of musical syntax. Music is a language just like English, French and Swahili. For starters, there are strong and weak beats in a measure with the first beat always the strongest unless displaced by an accent. The basic musical impulse is to move from weak to strong beats regardless of the notation.
Bar lines look like stop signs but are actually green lights.
Go from the last beat of the measure to the first beat. You would not use vibrato on a weak beat because it draws undue attention to it. Use vibrato to help show the strong beats. Your audience does not have the benefit of seeing the music so you have to show them by how you play what is on the page. The more clearly you speak the language, the more effective your performance.