A lawn mower very well could be a farm expense. However if it is also used to mow the grass of your residence, you have to apportion the personal and farm use. I am not sure that would be worth your time.
IF it is a riding mower, it may be worth while, but if it is a push mower, you are only talking about a few dollars when you start apportioning. ONe person I know apportioned a push mower between rental property and home use, and ended up with a depreciation deduction of 2.50.