royal tennis vs lawn tennis

royal tennis and lawn tennis both are nouns.

Word	Noun	Adjective	Verb	Adverb
royal tennis	Yes	No	No	No
lawn tennis	Yes	No	No	No

As nouns, lawn tennis is a hypernym of royal tennis; that is, lawn tennis is a word with a broader meaning than royal tennis:

royal tennis: an ancient form of tennis played in a four-walled court
lawn tennis: a game played with rackets by two or four players who hit a ball back and forth over a net that divides the court

Other hypernyms of royal tennis include tennis.

royal tennis (noun)	lawn tennis (noun)
an ancient form of tennis played in a four-walled court	a game played with rackets by two or four players who hit a ball back and forth over a net that divides the court