Northampton's Dylan Hartley then filled in for the injured Robshaw, leading England to a draw in their final Test against the Springboks in Port Elizabeth.
And Lancaster will delay naming his skipper until his squad assembles in preparation for the four-Test series against Fiji, Australia, South Africa and world champions New Zealand.
Lancaster said: "We haven't decided on the captain yet. We'll sit down when we meet in camp, we'll look at who's available in terms of form and fitness, obviously. Clearly Chris (Robshaw) has done a fantastic job. There's no reason why he wouldn't be strongly considered.
"If you look at the performance of the third Test, while Chris was missed on the field, Dylan (Hartley) did a fantastic job captaining the side.
"We got a performance out of the team in what was a challenging situation to make sure we finished the tour strongly, on the back of a long hard season for English rugby. That was credit to Dylan and also the rest of the players who played in that team.
"I wouldn't say the captaincy is overplayed - being England captain is a big job - but a strong leadership group is equally important. If you've got a fantastic captain but you haven't got someone who can run the game from 10 or run a line-out, you can forget it."