I have to disagree on one thing thought Tabarnak, you did not do bad. you had me really chaken for a bit, when I lost a city to your initial rush.
Now here is a hint. when you loose a city very early on like I did to Tabarnak it is important to not panic and waste to much resources trying to take it back.
If you tok liberty (you should) and got a few hills to work in the capital you should be able to build settlers in about 3 turns. Now If you look at what you lost. One settler (3 turns of producction) + mabye some producction of a worrior in that city (worrior max 2 turn in capital)
You lost 5 turns of producction in your capital (mabye 6-7 if you count the time it takes to move the settler into place), + some ground, If u do not replace the city however the loss will be great over time. (think about it like loosing a wonder a few turns from finishing except you dont get gold)
(loosing a city later in the game after building infrastructure, improving tiles, building gran and monument tec is a different matter thought and hurt a lot more)
So best thing to do if you see one city is falling, Try to make losses heavy for the opponent (If you kill 2 swords more then him you made up for the producction loss)
that is if you get a settler out ASP and place it.
So best move in my opinion when loosing a city is to make settlers in the capital and just replace it somewhere else on the map... (I replaced the city that fell with new ones against tabarnak, here is another hint, if u get Iw a bit late, try building a settler to be ready when u get Iw. In case u dont have ironworking on your pre mined hills or if its outside your culture border you might get some irontile close by where you can place the settler and still get iron fast)
Also like Tabarnak mentioned (and the reason he lost in the end) is that league duel is not only about swordrush, it is about beeing able to apply constant preassure and army producction while at the same time grow, build infrastructure, keep up with economy so that you dont loose scinece, mabye even sneak in a wonder.
you have to balance the short and long term because if you don t then you might hold off, even take some ground initially but loose in the long run.
Another good example of this balance from my game against Tabarnak, and how hard it is to make the right choises, is the reason I did loose a city early on against him. Like tabarnak said, Iron early is crusial. But...
The more technologies you manage to sneak in before taking IW the better for long term growth. Since if you get some luxery tech, like calander, trapping etc before IW then you can keep growing while placing more cities. However that means you will be vonourable longer. what I did against tabernak was taking (and in this order) pottery, animal husbandry , mining, calendar and Masonry before going for bronze working and IW (I wanted to sneak in the pyramids). It is allways good to know where the horses are early on. Horses means circus later on +2 happines. I also initially moved my settler for the capital a bit before placing it. This resoulting in that i did not only get Iw later then Tabrnak but also was unlucky and had my iron ion a hill outside culutre border and not on the 3 hills I had made mine on (in hope of one of them beeing the irontile) therefore I was without swords for a very long time. However, you could say I misjudged the situation and should have gone for iron earlier. however if you get away with taking some tech before IW it will benefit you in the long run. and you simply have to try to guess what your opponent is doing and how early he will strike....
Producction and money is king, but you cant neglect science and growth either. If you hit crossbows to late, say after turn 70 ish. You will most of the time have problems.
If you fall beind in producction, same thing.....
the really hard thing is to balance all this stuff...