I am assuming that L & I is labor or industries monies. What I. Am familiar with when I did food stamp eligibility was Workers Compensation. I assume these are the same. This is income that is countable under nearly every needs based income including food stamps and Medicaid.
List the income as the amount in the bi weekly amount and they will convert it to a monthly amount.
If your special needs son receives SSI, this is countable as well... If he receives SSI he most likely is eligible for Medicaid.
The only way you will know if you are eligible is to apply. Food Stamps is pretty straight forward.. It is based on income, assets, and household size. There are deductions for shelter costs ...
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The short answer is "yes". L&I time loss is income even though it's not taxable income. So report it, but also identify that it is temporary total disability money from L&I. Let them decide how to apply it. Keep in mind that if your time loss stops or your income changes, you can reapply.