Lewis is unbeaten in his three games in temporary charge, recording one win and two draws.
Lenagan said last week that the club were in no hurry to appoint Chris Wilder’s successor, but the U’s chairman suggested that the speed of the decision will be dictated by results under Lewis.
“I can imagine a scenario when we look in four-week chunks and review at the end of those four weeks,” Lenagan said.
“We will be looking at applicants, interviewing, but if Mickey carries on winning and returns two points a match on average, and we are still in the same place, we then review where we are again.
“One of the options open to us, and I am not saying I am going to take this option, is that if Oxford United continue to consolidate where they are in the play-offs or more preferably in the automatic promotion places, we could go to the end of the season if we are doing well.
“If we are not, we would quickly have to change. But we have to make sure we are ready to make that decision at the right time.”
Lenagan would not be drawn on any specific names, but reiterated that a new manager would have to tick all right the boxes.
“I am not prepared to discuss any particular applicants, but I would ask people to understand what style of person I am, in terms of who we are likely to accept,” he said.
“Nobody had heard of Chris Wilder and that selection board got it right.
“We now need a different type of person who can kick us onto the next level and can take us on to League One and above, but more importantly, fit in with the strategy and culture we want at Oxford United.”
Lenagan did not feel that Wilder’s departure from a team challenging for promotion to a side propping up the division reflected badly on the U’s.
But he is safe in the knowledge that a new manager will buy into the club’s philosophy from the word go.
He said: “Does it matter what people think about Chris Wilder joining Northampton? Not to me and I wouldn’t have thought to many Oxford fans. Who cares what the rest of them think?
“What a person decides to do is based upon his own personal judgement.
“I think with the way we want to run Oxford United, Chris did extremely well to try and do that, but it is easier to have your own man who will do it willingly because you have recruited him because he meets your cultural requirements.
“I had exactly the same situation at Wigan RL where in the first two years, I had a man who was a former Great Britain coach (Brian Noble), a long history of success in that environment, but I wanted a different style of manager and I got that. He (Michael Maguire) did exactly what I wanted him to do.”