Yes, lenders do require you to have your home owners insurance and property taxes included with your mortgage payment. Years ago they did not and when it came time for homeowners to pay there property taxes in one lump sum they did not have the money to do so. They also want to make sure the home is insured at all times.
Your payment is made up of Principal, Interest, Taxes, and Insurance. I hope this answers your question. If there's anything else I can help you with do not hesitate to call or email me anytime.
Have a good day.
Coldwell Banker United Realtor