Ok guys. Here is my report on Lima as promised.
I stayed in a hotel in Miraflores about 10min away from Kennedy Park.
First I tried two pet clinics directly in Miraflores. The staff in the first clinic told me that they won't sell H to private people and sent me away. The vet in the second clinic was very helpful. She looked under the counter and told me she currently hasn't got any in stock. She rang up two of her suppliers but was not able to order at that moment. Then she gave me the address of ConVet at Avenue Circunvalación and told me to go there as she would always buy it there. I thanked her and left.
Then I went to the National Stadium. You don't even have to take a taxi. The bus line 301 starting at Kennedy Park will take you there for 1.5 soles.
I went to ConVet, AgroSuni and that small shop mentioned by the PPH. None of them would give me the H without a prescription.
But I thought "no problem, the vet in Miraflores was so helpful, she will probably hand out a prescription" and planned to go there the other day.
This was day 1.