Britain have lost their last five Davis Cup ties, and face a relegation playoff against Turkey at Eastbourne in July to avoid dropping into Europe/Africa zone group III.
"Davis Cup Captaincy is a tough job and I'm sure that the next Captain will be as passionate as I was and have no doubt that the team is capable of defeating Turkey in July," Lloyd said in a statement from the Lawn Tennis Association.
"I have been a Davis Cup player, captain and now it is time for me to become a fan."
Newspapers decried the defeat in Vilnius as the most embarrassing yet. Lithuania have just three world-ranked players, all of them teenagers, while the LTA has an annual budget of more than 50 million pounds ($76.79 million).
Andy Murray, who did not play in the tie, is the world number four and the only British player in the men's top 100.
Britain have won the Cup nine times although appearing in only one final since 1937.
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