Last month, organisers said the tour would go ahead as originally planned, with the first Test scheduled for July 24, and Roux suggested that they were still working towards a best-case scenario.
"We are obviously looking at a number of different contingencies around what happens if Covid-19 continues in the way that it currently does," Roux said at a press conference yesterday.
"First prize is that that doesn't happen. Second prize is that there are some restrictions and we can manage in those.
"To be fair, no spectators and an inability for people to travel would commercially not make this viable and there would be a serious -reconsideration on how we then continue in terms of the tour.
"In the build-up to this, in the past couple of months, there was some consideration given to moving it. We decided on the best-case information we have and that is that, in all likelihood, by June next year travel would have returned to what is deemed normal and that we will be able to continue."
A postponement or cancellation would be financially calamitous for both the South African Rugby -Union and the Lions.
The 2017 tour generated a £20 million profit for the New Zealand Rugby Union and £7 million for the Lions, which is split between the home unions.
The Daily Telegraph understands demand for tickets from home fans is on course to outstrip previous tours.
The South African Rugby Union yesterday announced that tickets would be on sale for as little as £4; however Roux said that any tickets bought would be reimbursed in the event of matches not going ahead.