Do I claim insurance payments I received for lost income because my business activities were halted?

Yes.  Insurance payments received from loss of income would be considered taxable income.

The IRS IRC. section 61, states that gross income is defined as any income derived from any source.  Since the insurance payments are payments being made for income that would otherwise be taxable, the proceeds would be considered taxable.  

If you are filing a Schedule C with your 1040 return, you would enter the insurance payments by following these steps:

1. Click Wages & Income
2. Click Add/Edit on Self-Employment
3. Enter the interview questions regarding the business
4. Choose Other self-employed income

Here is a link to what is considered taxable income:

What is considered taxable income