Lampard took the side that won Europa league, finished 3rd in the league. Lost Hazard but added players like Pulisic, Kovacic (loan to permanent), Tammy, James, Mount, Zouma.
It's not as if ManUtd added world class players, the player we signed from Championship wasn't better than Mount, most of the Chelsea fans even said how Reece James was much better than AWB (some argued he was as good if not better than TAA)
This "manager x spent yz millions" always lack context. So ManUtd had to spend around 60 million to sign players who aren't as good as Chelsea loaned out players who returned in 2019 summer.
Also Chelsea only Hazard from their starting 11 (he was arguably best in the world, so big loss). ManUtd lost Herrera, Smalling, Lukaku who were all part of our best 11. Of course they weren't as good as Hazard but then we don't have anyone who was as good as Hazard to lose.
Arguments can be made on both sides easily, people talk about transfer ban but completely ignore the players who all had few years experience out on loan (these players had more experience than ManUtd players like AWB, James, McTominay). Just like how Chelsea squad had lot of doubters, ManUtd squad had too, saying we don't have any attacker capable of scoring 20 goals and we sold the only player who is capable of it. We didn't replace Herrera, McT and Fred are not good enough.
Both managers did good job in shaping the squad, whoever takes over will have much better squad than what Lampard and Ole had.
Edit: Thought this was Ole vs Lampard thread. We have dedicated thread for that.