'low-billed' is a modern English compound formed from 'low' + the past-participle/adjectival form 'billed' (from the verb 'bill'), where 'low' meant 'not high' and 'bill' referred to a beak or an invoice/charge.

'low' comes from Old English words meaning 'not high' and developed into modern 'low'; 'bill' (the verb/noun) comes from Middle English 'bille'/'bill', and the adjectival form 'billed' (past participle) combined with 'low' to form the descriptive compound 'low-billed'.

Initially the components separately meant 'not high' and 'beak' or 'invoice'; over time the compound has been used descriptively in contexts such as ornithology ('having a low/short beak') and in commerce ('having a low charge'), keeping the core sense of 'low' applied to 'bill'.