Under EASA regs who is responsible for part m continued airworthiness? Lessor or Lessee?
It really comes down to the lease contract.  I don't think any of the regulatory authorities much care who pays to maintain it or what's in the lease contract, as long as the airplane is airworthy when it leaves the ground, which is basically up to the operator.  What we are really talking about here is who pays.  

Pretty much anywhere, the lessor is expected to deliver the unit in an airworthy condition, then the lessee is expected to maintain it and return it to the lessor in an airworthy condition at the end of the lease. Like a car.  But it depends on the details in the lease.

The lessor is frequently a non-operator (Like GE Capital) who has no means to maintain the airplane in the first place so in any case it's the airline that will actually do the work, or contract the work, for something like an AD.  

Who is on the hook to pay for Service Bulletins and AD compliance will be up to the lease contract (on an aircraft that is out of warranty).  If someone leases an out-of-warranty airliner from GE Capital, and the contract says that GEC will pay for ADs, then the airline will do the work but charge back the expenses to GEC.  

Plus, GEC may have a clause in its purchase agreement with the OEM to cover AD costs beyond the warranty period and extend that protection to the lessee.  There are large variations in terms and conditions between OEMs, leasing companies, and airlines on a given type, as it's all part of a negotiated package.