Is the Davis Cup associated with tennis or lawn tennis?

Traditionally, tennis was viewed as a game to be played mainly on the lawn.
As a result, most earlier tennis clubs or associations were named as 'Lawn tennis associations".
In Australia, for instance, the tennis association, not so long ago, was named, the LTAA or the Lawn Tennis Association of Australia.
Originally, the Davis Cup was seen as mainly a lawn tennis tournament, but it has now moved along with the times, and can be played on various surfaces.