In message , Janet Baraclough
writes

Buddleja and Buddleia are both accepted spellings (so far as I
know); and the pronunciation is the same. I don't write or think
Buddleja because I think it's a clumsy word shape, though at least it
should remind me that the E comes after the L :-)

Janet.

AFAICT, according to the rules, Buddleja is the correct spelling, but
I'm not able to find a clear exposition of the situation. IPNI
(International Plant Name Index) has Buddleja, and refers to Kew
Bulletin 349 (1928) for a note on the subject.

Linnaeus used the spelling Buddleja.
--
Stewart Robert Hinsley