Squats and lunges will help improve the strength of your quadriceps, glutes, and hamstrings. That said, squats and lunges alone might not be the sole reason for the sensation of fatigue you experienced. However, incorporating strength training into your running routine is a great idea regardless. 
Hi Susan- I live in the Chicago area and did my first marathon last fall in Indianapolis. I’m 52 and my time was 4:01:05 and I was happy with that but want to break the 4-hour mark. Around the 21-22-mile mark my quads started burning. Would doing more squats and lunges help me improve in that area? Thanks for your time, David Hey David- Thanks for your question and congratulations on your marathon! A four-hour marathon is a great time!
Source: How to Prevent Marathon Fatigue
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About The Author
Dr. Nick Campitelli
Dr. Campitelli is a podiatrist in Akron, OH specializing in foot and ankle surgery with an interest and enthusiasm for running as well as helping runners with injuries. For the past several years he has been treating running injuries in patients by fixing their form and transitioning them to minimalist shoes. Having treated runners with all types of injuries through conservative measures with orthotics and shoe gear changes to reconstructive foot and ankle surgery, Dr. Campitelli has brought what works best and is most current to his practice as well as the Akron and Cleveland running communities.