If I look ahead at the 2023 cap, and we assume it'll come in around $225M in total, Lamar's cap hit would put us over the cap by about $6M. And that's with only 43 players under contract.
The main cap savings I would see are:
Boyle : $8.3M. He's either getting an extension or is getting cut next year, regardless of Lamar's status. Can't have a $10.3M cap hit for a blocking TE.
Zeitler: $6.5M. Hard to see him as an extension candidate, so he's either a cut or a keep. If tight against the cap, cut seems likely.
Campbell: $6.5M. Imagine he retires or isn't brought back anyway.
Edwards: $4.4M. I imagine he'll be gone in almost all scenarios. Especially if he can't recover from the injury.
Clark: $3.3M. He might also be gone regardless.
So even if I exclude Zeitler for the moment, you can clear about $22.5M in cap space from releasing Boyle, Campbell, Edwards and Clark. And you can make a case you've either got replacements or can easily replace some of these guys already.
So that wouldn't make the cap in dire straights. BUT... that still only leaves you around $16M, which isn't a lot.
Now, on the flip side, if Lamar signs before then, and his cap hit for next year is, say, $30M (probably would even be less), you can still move off these guys AND have upwards of $30-40M in cap space to play with. Now the floodgates are open. You can basically sign anybody you want.