'sustainably-managed' is a modern English compound combining 'sustainably' and 'managed'; 'sustainably' derives from 'sustain' + adverbial suffix '-ably/-ly', and 'managed' is the past participle of 'manage.'

'sustainably' ultimately comes from Latin 'sustinere' (via Old French/ Middle English forms of 'sustain'), where 'sus-' (variant of 'sub-') + 'tenere' meant 'to hold up'; 'manage' comes from Old French 'manegier' (from Italian 'maneggiare'), from Latin 'manus' meaning 'hand', evolving into Middle English 'manage' and then the modern verb 'manage'; the compound 'sustainably-managed' arose in contemporary English usage to describe operations run under sustainability principles.

Initially components referred to 'holding up' (sustain) and 'handling by hand' (manage); over time they combined into a phrase meaning 'handled or overseen in a way that maintains resources long-term' and this is the current usage.