This is an out-of-scope question, but let me give you some direction.
The city of Los Angeles imposes taxes on persons engaged in any trade, calling, occupation, vocation, profession, or other means of livelihood. Which implies active engagement in an activity. From what you are describing, it doesn't sound like you are actively engaged in a business activity anymore.
Even if the state taxes income from out of its area, it still needs to be an activity you are actively engaged in. But you seem to be describing passive income received in the form of royalties.
I suggest you contact LA Office of Finance (the contact information should be on the notice you received), and explain the situation. Also, make sure that you inform them that the business is closed. Read more about it here.
For the future, be aware, that there are a couple of exemptions from tax that you may qualify for. Read about it here.
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