Carl Baker opened the scoring for Coventry before Lisbie and Dean Cox gave the O's a 2-1 half-time advantage.
But although Baker was sent off for a dangerous challenge on Romain Vincelot in the 55th minute, Franck Moussa equalised four minutes later for the visitors.
Leon Clarke then squandered the chance to restore Coventry's lead when he had a penalty saved before Lisbie's last-gasp header from Moses Odubajo's cross settled the tie.
"I'm glad it was in the ninety because, for sure, we didn't want another thirty,'' Slade said.
"For the neutral, I thought it was a great game, but it wasn't for me at times because sometimes, our defending uncharacteristically was not the greatest.
"After the penalty save, we rolled our sleeves up and that spirit that we've got, the focus and commitment, all came out and there was only going to be one winner I felt in the last 10 minutes.''
Slade acknowledged his side showed plenty of character. "We managed to dig in and show great, great spirit, which is what the group is all about if I'm honest and we hung on in there,'' he added.
"The first 25 minutes belonged to Coventry and they deserved to get their noses in front, but we hit back quickly and that settled us down.
"It was a cracking cup-tie. You don't see too many round one ties like that, so credit to both teams who played their part.
"But the important thing is to get through, which we've done. It would be nice to get a big tie at home in the next round and hopefully fill the stadium.
"We've won our first league game of the season as well and the key thing now is to recover in time for the match with Shrewsbury on Saturday.''
Despite the defeat, Sky Blues manager Steven Pressley praised his team. "It was a superb performance from us,'' he said.
"We played exciting and high intensity and high energy football and how we didn't win the game in the end is a bitter blow.
"We made a magnificent start, you heard the supporters singing 'Only play like Brazil!'
"The players were magnificent and if I was a fan, I'd be exceptionally proud of the team's performance.
"I didn't think Carl Baker should have been sent-off because I don't think his foot came off the ground.
"Although his studs were showing, they were on the ground. But that shouldn't overshadow the performance of the players.
"If we play with that energy and confidence, we'll win plenty of games. I don't think the players can give any more than they have done so far and I'm extremely proud of them.
"The reception that the players got from our fans at the end of the game very much summed up what they thought of the performance and we are all very disappointed with the result of the game and we wanted to progress to the next round of the cup.''