"Lawn tennis" was the name by which tennis was previously known worldwide, as it was always originally seen as a game to be played on grass.
Even today, the most prestigious tennis tournament in the world - Wimbledon - remains played on grass.
As for skills relative to it:
It was generally stated that the most important 3 shots in lawn tennis were:
The serve
The First volley, and
The Return of serve.
Due to the fact that it is considered a skimming, "fast surface" ... that the ball stays low, with the occasional bad bounce, it is usually believed that the best style of play on this surface is the typical "serve and volley game".
As such, the "basic skills in lawn tennis" are serving and volleying.
Because the ball skims through off the grass fast and low, sliced ground stroke shots are also as useful as the top spin - more commonly employed today, and the ball is played low over the net most of the time.