Is it illegal to lie on food stamp application?

Yes, it is considered fraud. If you are successful in obtaining food stamps based on false information, you can be prosecuted. See the link below. A quote from that page, 'Unlawful possession or use of food stamp benefits in an amount of $100 or more is a felony; less than $100 is a misdemeanor.' The amount of your offense would be the total amount of the benefits that you received fraudulently.