Horta-Osório (pictured) took a leave of absence on medical grounds at the beginning of November, reportedly suffering from severe exhaustion and stress, and is expected back by the end of the year.
Group finance director Tim Tookey has stepped in to act as chief executive in the interim, but will leave in February to head up Friends Life.
As a result, Lloyds has confirmed Roberts, a non-executive director since 2010 and chairman of its risk committee, will become interim group chief executive if Horta-Osório is delayed in returning to work.
Sir Win Bischoff, chairman of Lloyds Banking Group, said: “The Board is pleased that António is making good progress and we are looking forward to his return at the end of the year.
“However, we recognise it is important that we formalise the contingency arrangements if António’s return is delayed.”