In Entertainment Management class (going on 20 years ago now), we were told that these things are left to the individuals involved, their agents, and their lawyers. Royalties are given to all persons listed as authors, but I don't recall any specific stipulations for order or attribution of lyricist/composer.
As for Lennon and McCartney -- all four Beatles have given numerous interviews wherein they discuss who wrote what. George Martin, their producer, has done the same. Hunter Davies, their biographer, actually sat in on some writing sessions and reported them in his book. Numerous other observers have also chimed in. The unanimous conclusion: both John and Paul wrote both words and music. In the early years they tended to do so fairly collaboratively. But by the Help! album (1965), John was writing both words and music to his songs, and Paul was writing both words and music to his songs. During rehearsals and recording they would all make changes and refinements, but the primary author was just that -- the guy who wrote most or all of it.
"One thought driven home is better than three left on base." James Liter