Both can be dual nationals.
Archie is British other than by descent, as he was born in Britain to a British parent, whereas Lili is (probably) British by descent as she was born overseas to a British parent.
(If however Harry was, at the time of her birth, on a crown service/diplomatic/head of state official visa, then it is perhaps possible that Lili could also be considered British other than by descent (same pattern as DC born to eg diplomats and armed forces personnel during overseas postings)).
Those two types make no practical difference to the Sussex DC, but it would affect the entitlement of their descendants to claim British nationality if A&L remained overseas and their descendants were born outside Britain.