A lawn needs a level surface for easy mowing. Slopes are dangerous to mow with powered equipment and petrol mowers are limited to slopes of 30 degrees or less, unless they have a 2-stroke engine fitted or a modern 4-stroke designed for this use (eg some Honda engines).

But a 30 degree slope is no fun to mow, so consider planting it up with something else. You could try thrift, which remains neat, looks like grass from a distance and has the bonus of pink flowers. Or heathers, which have a variety of leaf and flower colour, and flowering times, but will need shearing at intervals to stop them getting straggly.