It depends on what the agent should do in Apollo.
API Key: enough for enrichment, organization lookups, and creating or updating contacts and accounts.
Master API Key (optional field; only Apollo admins can copy it, in the Master Key section under Settings, then Integrations, then API Keys): needed for people search (prospecting) and for sequences, deals, tasks and calls. Without it, those requests fail with a 401 error.
Weekly prospect scan: this scheduled task needs both Apollo and Lemlist, and relies on people search, so add the Master key if you want prospecting.
403 means your Apollo plan doesn't include API access; 429 means Apollo's rate limit, so space out the runs.
Saving the key restarts a running agent. More: Apollo integration.