Having been to both Lisbon and Barcelona, I would recommend 4/5 days in each, however this of course can be reduced/extended depending on your preferences/interests.
Your flight gives you 11/12 days in Europe, depending on your flight times. Given this is a relatively short time, and that there is so much to do in both Lisbon and Barca, I would not recommend flying out to Monaco or Italy, and instead make the most of the places that you are going!
If you wanted somewhere to add into your itinerary, you could either stop off somewhere between Lisbon and Barceloana to break up the journey - Madrid is an obvious choice, although I would also consider the Andalucia region of Spain, as Grenada/Seville and the surrounding areas are meant to be fantastic (though I have not been myself).
Alternatively, you could use the extra time to go on day trips from either Lisbon or Barcelona. With regards to Lisbon, I would definitely recommend Sintra, it is only a 45 minute train out of Lisbon, but is simply fantastic. As it is May/June it is also perfect beach weather in Barcelona if you are that way inclined.
If you are getting trains in between destinations, I would recommend trying to get overnight trains, as this gives you more time in the destination (and saves money on accommodation). However, I have never used trains in that region myself as I am from the UK so have just been to Spain and Portugal on short trips straight out of London.
In short though, I would definitely recommend making the most of Spain/Portugal, and leaving France and Italy for the next trip - there's so much to see there, a few days will definitely not do it justice, and you'll be spending even more time in airports.
Hope This Helps