Creative activities in The Sims 4 are quite profitable in the long run. If you play without codes for money, surely at least one of your Sims is engaged in at least one of the types of creativity offered in this part of the game.
As far as music lessons are concerned, without getting a proper job, they won't initially earn any Simoleons unless you play for tips in various community lots. But it should be borne in mind that playing for tips is available only to guitarists, and only if they have at least the third level of guitar playing skill. For violinists and singers, there is also an opportunity to earn money: just start playing the violin or sing, and Sims passing by will begin to “tip” your musician. But there is no way pianists and organists can make money from tips, and for musician Sims playing other instruments, this "earnings" are unlikely to be enough.

Thus, the most profitable way to earn money is to publish works of your own composition, and for this you need to know how to compose a song in The Sims 4. This article will help you with this.
How to compose a song in The Sims 4 with guitar and violin

When you upgrade your guitar skill to level 8, you will be able to compose songs using the action that pops up in the menu when you click on the guitar. The songwriting process takes 12 sim hours, but it is not necessary to compose a song in one go. If you have not finished, you can continue by clicking on the notes that will appear in your luggage as soon as you start composing again. You can sell the rights to your songs from the 9th level of the guitar skill. In this case, you will receive roy alties daily, but you will be able to publish a new song only after one sim week.

The same way it works for violinists.
How to compose a song in The Sims 4 on piano and organ

To compose music on the piano, synthesizer or organ, you must have at least level 8 skill in playing the instrument. With level 9 playing skill, you will be able to publish your work and receive roy alties for it under the same rules as guitarists and violinists.
Sims 4 Singers Composer Options

Sim world vocalists can compose songs from 8th level of singing skill and publish them from 9th, nothing special here. However, unlike other skills, the singing skill can be used to compose songs with instrumental accompaniment. Thus, if you have at least level 8 singing skill and at least level 3 skill in playing any instrument (except organ), you can compose songs for vocals and, for example, guitar.
As you can see, there is absolutely nothing difficult about songwriting in The Sims 4.