The Bible doesn't say anything about mowing a man's lawn, so I'm not going there. The Bible does say the cares of this world can choke the word.
29“The most important one,” answered Jesus, “is this: ‘Hear, O Israel: The Lord our God, the Lord is one.e 30 Love the Lord your God with all your heart and with all your soul and with all your mind and with all your strength.’f 31The second is this: ‘Love your neighbor as yourself.’g There is no commandment greater than these (Mark 12:29-31 NIV).
I like my lawns to be mowed regularly to make my house look tidy. To love my neighbour as myself could involve mowing his/her lawns. That's a practical demonstration of what it is to be a good Christian neighbour.