Coventry beat Wrexham 3-1 on Sunday to lift the trophy in front of their home supporters, finishing on 92 points and 12 clear of nearest challengers Ipswich Town. Lampard's side scored eight goals in their final four games after sealing promotion at Blackburn.
"It is a massive challenge, right? We see with the amount of teams that go up and come back down, it's a big step, and to get any foothold in the Premier League is hard."
He was candid about the pressure to act immediately.
"We've got a lot of work to do. We'll do it quickly, and I think I feel like we have to do it quickly. It's the owner's choice on a lot of these things because he's the boss man in the football club. But the conversations obviously have to happen quickly, but also enjoy this little moment."
One deal is already done — loan striker Frank Onyeka has joined permanently — and the club are working to secure a permanent deal for goalkeeping loanee Carl Rushworth.
Lampard also allowed himself a moment of reflection.
"It's amazing, right? This league's so tough. We know that, lived it and this team, the boys have gone, and now they've dominated the season in terms of the points that they've racked up. It's a special year crowned off and topped off at home with lifting a cup. Great, amazing."
Burnley, the side Coventry pipped to the title last season, have been relegated in their first season back in the top flight. All three promoted clubs from two years ago suffered immediate relegation.