On the first two weeks, while it is possible, it is not very likely to win unless you are lucky and / or willing to reload a lot. By the third week tho, even if you are a bit unlucky, you can have the mining pickaxe, the chainvest and the glacial buckler which makes fights winnable. I got a rejuvenation bead too, which makes the fights against Irelia a default win and Katarina and Qiyana are also quite beatable without anything else. The updated Lux can be tricky and i suspect that some magic resist based gear is needed.
Very important: Avoid fighting Ahri at all cost! She has a skill that drains your attack permanently which can make combat simply impossible.
Similarly avoid Qiyana until you are geared up properly, because losing to her can seriously nerf your character as well, tho at least this doesn't stack like Ahri's punishment does.