I have sat through hundreds of musical theatre auditions for community theatre productions, either as a producer, director, or stage manager. I can tell you that for amateur performers there is a marked delineation between the auditioners who have had competent teaching and those who have either not benefited from lessons, or who have had bad teachers. This is true for all three aspects of the musical theatre audition: singing, dancing, and acting.
The thing about lessons for all of those disciplines, is that your teacher will help you to find pieces that are suitable for you. This is a valuable service that they offer, bringing their broader range of knowledge to serve their client. Your vocal teacher will be able to find a piece for you that you can master, and they will help you to master it before your audition.
1. Choose musical theatre pieces. This sounds simple, but too many times, I sit through an audition that is lacklustre because the actor chooses a popular song. I would quite honestly rather hear a really proficient rendition of 'Twinkle Twinkle Little Star' than "Hey Jude" any day. And I love The Beatles, but without the backup vocals and instrumentation behind it, the song is not very wide ranging or entertaining.
2. Play it safe. Auditions are not the place to try to hit that high 'C' unless you have absolutely no difficulty hitting it every single day. You want to show your ability, but unless you are certain of every single note in a song, then you need to choose something else that you can hit every time.
3. Bring it to life. Think of your song as musical monologue and put something of a character into it. Your goal is to show the director that you can sell a song: so sell it!
Remember that the purpose of an audition is to show off what you can do best. So prepare, prepare, and prepare. Ask for help, ask for pointers, use your teachers, your friends, your fellow actors and get some objective, constructive insight so that you are ready for your audition.