We totally loved Lillian's apartment and highly recommend it!! It is very beautiful, comfortable and clean. It is also very well equipped (including for a toddler), calm and at walking distance (approx. 15-20 min) from all historic sites.
Eleni was very helpful and responsive with the pre-arrival arrangements, Anastasia welcomed us warmly upon our arrival, and Panos responded competently by phone when we had an emergency (see below). We are very thankful to all of them! We also very much recommend taking the reliable and friendly taxi driver which they work with.
Once piece of advice: Make sure to ask for written instructions for how to handle the keys upon your departure and that you understand them well! We got locked out of the apartment, without being able to get out of the building's main door.