A pivot table won't work as you have correctly identified it works with "summation" of numbers...
If you list your unique lab_id in column I as you did (you can use advanced filter to get unique list) and then list the Round numbers in Row 2 as you did (except you should only show the number (5) instead of "Round 5"), then you can use a formula in J4 like:
copied down and across.
Make sure you don't use ranges that are much larger than you actually need as this is a bit of a resource intensive formula.
A much better way would be to add a helper column with formula:
copied down alongside your database.
Then use formula in J4:
copied down and across, where column G contains the concatenated helper column
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