Notes

I'll just compile everything easier
1) Aggressive position lvl 1-2 really shoved in, very easy for jg ganks. Lucky the vi went mid instead. Try to be aware that you are very pushed and tell your adc to back off a bit unless you have vision in your river bush (pref the tri/in between the 2 bushes on the river to get max vision if the jg comes from river)
2) Nice aggro to get the lucian early but should had shot q straight up to get confirm stun before w. you prob waiting for him to dash but messing up the combo. At least you got a return kill on alistar
3)Should get tier 1 boots at least for mobis instead of saphire crystal. Mana won't be an issue if you conserve a little
4) Nth could had prevented the 2nd death but should push your pink ward to the tip of the bush nearer to dragon pit so have more reaction time against vi (plus no flash up don't extend your push-> mainly adc for not noticing but gotta just type care jg)
5) The pink ward caught the sp going towards the river fight, should had join the river fight there which you could had done sth to get an assist or 2 maybe a kill. Honestly against lucian who is very mobile and surprise burst with full combo, you should just hug turret a be very behind if you have no flash.
6) Should stand towards the side of adc instead of behind to assert some dominance
7) Good roam to mid when your lane is pushed up and you got a kill on vi there
8) Be aware if your jg is nearby and looking for a gank. Since your lane was pushed up, you could start to initiate the fight earlier so the bot lane would had less time to react to the gank. Could had killed lucian there
9) Should had b instead of shoving the wave that is under your opp turret if you know you cant get the tower. Lost first tower because of that. Can't do much cause you are not 2 players. Should ping your adc to b there
10) Should flash r q on the garen that was under turret, good idea but risky as it was a 3v5 and your damage not that much yet. Didn't need to force that too but at least no one died
11) Look at map and see how many was fighting at top. You recalled while the enemy team was still at top while your adc was trying to get the 2nd turret down. Could get more gold if you hit the turret more :P But ye, could save some time there if you join your adc in shoving the 2nd turret. Thankfully you did notice taht.
12) Can w the back wave and it brings it low enough for your adc to hit them all. Shoves faster that way
13) Usually when you r, try to follow up with q instantly to get stun there. The fight at the red buff there could had gone either ways. Lucky nth happened
14) Should had rushed to baron. kai sa can rush baron down fast
15) Really need to press q after r LUL. Need that stun then w for guaranteed bonus damage
16) Should either spam ping your separated members to back off or tell your team to join them. Try not to split cause their team can rotate faster than you
17) Nice comeback hmm that triple inhib was really beneficial for you