What JSON Lines is
JSON Lines is one complete JSON object per line, with no enclosing array and no commas between records. The file is not valid JSON as a whole, and that is the point.
Log pipelines, machine learning datasets and anything that appends records or reads them in a stream.
What BBCode is
BBCode uses square-bracket tags. Table support is not universal, but table, tr, th and td are widely implemented.
phpBB, vBulletin and forum software descended from them.
What changes when you convert JSON Lines to BBCode
Each line is parsed on its own, so a corrupt record does not take the file with it. Keys are unioned across lines in first-seen order, so a record missing a field leaves that cell empty rather than shifting the columns.
Check that your forum has table tags enabled. Many boards ship with them switched off.
What carries over from JSON Lines to BBCode
JSON Lines records 5 things about a table that BBCode has no way to hold.
JSON Lines distinguishes a number from the text of a number; BBCode does not, so every value arrives as text and has to be re-parsed by whatever reads it next.
An empty cell and a missing one are the same thing in BBCode, so a null and an empty string in the JSON Lines both come out blank and can no longer be told apart.
JSON Lines can hold a value that is itself a list or an object. BBCode has only flat cells, so nested values are flattened into one cell rather than being spread across columns.
The keys stop being repeated: BBCode writes the column names once at the top, so the same table takes noticeably less space.
JSON Lines can be read one record at a time. BBCode has to be complete before it means anything, so the whole table is held in memory while it is written and a file that gets cut off part way through is not partly usable - it is unusable.
BBCode is the end of the line for this data. Reading the table back out of it is a separate and much harder problem than writing it, so keep the JSON Lines if you will need the values again.
The identifier 007 comes out of the BBCode as 007. Reading it as a number would have made it 7, and an id that changes value is worse than one that stays text.
The role "Analyst, data" survives with its comma, in one cell rather than split across two. That is the first thing to check in any converted table, and the usual place a BBCode file goes wrong.
The quotes around Jonah "Jo" Pryce are left as a plain quote character in the BBCode.