1.) spacing vs lucian - you always want to be on the same side of the lane as lucian (i.e. both top, both bottom) so he can't piercing light you. you often stacked up with me (i was playing opposite side of lucian) which led to awkward/easy peircing lights. might have been for last hits, but you have to try to approach it a little better
2.) aggresive trading/positioning: you actually had a few really good moments of aggressive trading *after* he wasted a piercing light etc, but you often extended them for 1-2 autos too long which led to your positioning being awkward (on top of minions/weird place in lane) and taking damage you didnt need to. vayne excels at 1/2/3 AA trades totally situationally.
3.) we overstayed in lane. better off giving up a minion wave, nami is literally useless without mana + you were low hp. better to go back, lose the minion wave, come back fresh when they go back and both lanes will be 6 + shopped. i had to spam my heal on you which is not effective (nami is much better off aggressively using her W on the enemy to get multiple bounce procs etc), and kept me mana starved
4.) the level 6 all in. unlikely you were gonna win your lvl 6 all in while i was lvl 5 and oom and sona was 6. mechanical misplay by not flashing/tumbling sona ult (which is hard but entirely doable), which then led to your quick demise. this was a massive risk play with like 1-10 odds of working out, and if it failed (which it did) would have snowballed the lane heavily against us. lucian is able to bully vayne without an advantage so with an even bigger one, you pretty much are designated to farming under turret