I'll lend you this CD on the condition that you don't pass it on to anyone else.
Literal
Re-lend don't do condition [with-で] this CD [object-を] lend-[for-you-あげよう].
又貸し ('re-lending, lending-on') is a noun formed from 又 ('again, additionally') + 貸し (stem of 貸す 'to lend'). 条件で ('on the condition of') is the standard way to attach conditions. 貸してあげよう uses the volitional of あげる — 'I'll lend (to you, for your benefit) .'