M7 Vi here(just need the essence ;-;) let me see if I can break it down for you.
The level one trade that you lose Auto>E>auto>Tlords>E
E is an auto reset, so she got a quick burst on your to proc Tlords. It can hold 2 charges. It's also an AA modifier which at level 1 adds 10(+115% AD) damage.
Assuming she started longsword 3, and had attack marks and quints, that's 15.3 AD(from runes) and 10 AD(longsword) added to her base AD of 55.9 at level 1 means she has a total of 81.2 AD at level 1.
That means that Auto>E>Auto>Tlords>E is roughly:
81>103.15>81>17.59>103.15 damage. That's before any mitigation though.
Talon at level 1, has 583 HP, and 26.9 Armor, assuming you had the standard 9 armor, (and 9 MR since Tlords is magic dmg so that's' 41.1 MR)then you had 35.9 Armor.
Then after mitigation it becomes 59.6>75.9>59.6>12.4>75.9=283.4 damage
So you lost 283 of your 583 HP, dropping to 300(you lost about roughly 50% HP) You also took damage from minions though, which was actually quite a lot.
You died during the level 2 trade. When Vi went in then it looks like you have about 40% HP, so about 233 HP.
She started the engage with Q. Q has a base damage of 40(+60% bonus AD) but that is increased against champions so it was 50(+80%bonus AD) it also knocked you back, stopping you from retaliating immediately.
Assuming she still only has one longsword, Q would do 70.24 damage, since you were level 2 your armor was then roughly 39 so Q did 50.5 damage.
She followed Q with an Auto followed by E which procced Tlords again.
her auto at level 2 would do 60.4 dmg, E then did 76.7 damage, and Tlords did 39.9 damage
That's a total of 227.5 damage. Since she killed you, I can only assume she had armor pen in masteries, which accounts for the approximate 5.5 dmg I missed here.
It's totally feasible for her to that much damage. She has very high numbers. You got cheesed by an extremely off meta pick. Vi is played in jungle because it's very hard for her to win fights in top lane. Her Q is her only engage/escape and it slows her when charging, she's very susceptible to being poked out f lane, even with her shield passive.
I don't know for certain, but she probably set up her runes and masteries specifically for mid, I don't play vi out of the jg, so I couldn't say what they are. But yes, Vi SHOULD do this much damage. You just got cheesed hard.