Lycett was the recognized as one of the dominant players in men's doubles. He was the champion at both the Australasian Championships and Wimbledon multiple times.
His cousin was the operatic soprano Miriam Licette.
- Austalasian Championships (2): 1905 (w. Tom Tachell), 1911 (w. Rodney Heath).
- Wimbledon (3): 1921 (w. Max Woosnam), 1922 (w. James Anderson), 1923 (w. Leslie Godfree).
Mixed Doubles (3):
- Wimbledon (3): 1919, 1921, 1923.