A single search could do it:
| fillnull username, src_ip, browser_agent value="unknown" | dedup username, src_ip, browser_agent | table username, src_ip, browser_agent | outputlookup lookup1.csv
Your lookup could then work like these:
| lookup lookup1.csv username OUTPUT src_ip, browser_agent
| lookup lookup1.csv src_ip OUTPUT username, browser_agent
| lookup lookup1.csv browser_agent OUTPUT username, src_ip
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