Line maintenance is on-going stuff like oil, filters, igniters, tyres etc and any defects that arise in daily service, plus a basic inspection schedule. It is usual for the lessee to be responsible for that.
Shop visit costs for major work on engines, landing gear etc should be covered by an hourly rate within the lease document and may be lessor's responsibility (but check the fine print) because some lessors like to have control over the quality of big-ticket work. Often the lease will state that the aircraft will be delivered at a certain stage of its airframe check cycle and must be returned at the same or at another agreed status at the end of the lease. e.g. delivered with fresh 'C2' check, returned with same or maybe a fresh 'C3' if that is the next one due in the cycle.
Your company needs to have someone who knows what they are about do the acceptance. All too often people get all excited about a new toy and don't do their homework. An operator I once worked for ended up having to wear the cost of a very expensive engine because they did not do the appropriate acceptance tests. One engine did not have a very good EGT margin and it rapidly got worse in service, so that when it came time to return the aircraft the lessor insisted on compensation.