Answer: There are several ways to kill a lawn. One would be to use an herbicide containing glyphosate. Read and carefully follow all of the label directions. Another would be to smother it under newspaper and a thick layer of mulch. You could spread about five sheets of newspaper (overlap the edges so it is a complete cover) and put the mulch on top.
I should mention that gravel will reflect heat in summer, and weeds will grow in it very happily unless you rake it often. A mulch layer will need to be raked and refreshed (more mulch added) quite often, and weeds will grow in it if you do not maintain it that way.
You might find that a groundcover is a good solution. However, this type of planting requires good soil preparation, then it needs watering and weeding between the plants for the first year or two until it becomes established.
I hope this helps in your decision process.
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