Woo. And after a long day, I will now publish my argument, which I have put some effort into. So, here it goes!
Ok. I reconsidered my argument with the new information that came to light, and my argument will be done from a different perspective: looking at how the battle starts.
But I should compare what both Jotaro & Lucy are capable of first:
Jotaro & SP
+ Superior strength
+ Superior durability
+ Can't be interacted by Lucy's vectors
+ Superior intelligence
= Just as cunning
= Microscopic precisio
= Can negate durability
- Doesn't naturally go for the kill immediately
- Inferior melee range
- Inferior hax
- Inferior mobility
Lucy
+ Superior hax
+ Superior melee range
+ Naturally goes for the kill immediately
+ Superior mobility
= Just as cunning
= Microscopic precisio
= Can negate durability
- Inferior strength
- Inferior durability
- Can't interact with Star Platinum
- Inferior intelligence
It does show that this match is fairly even and given the circumstances, it can go either way. However, for this circumstance, I see Lucy taking this more often than not. Here's why:
Right off the bat when they spawn, they will look at their respective opponents. Lucy's impressions of Jotaro won't matter too much because she'll try to kill anyone no matter who they are. Jotaro, on the other hand, will see an underweight and underage girl with 'long cat ears' that is 1 whole foot shorter than him and seem like she's easy to kill (she has a petite physique). With that in mind, he's likely to consider going for incapacitation. Considering the starting position the OP specified for us, there would be no objects within his reach that are easily accessible (as it is just flat grasslands, meaning not much objects to pickup if he considered it as the trees are too far and whatever objects there are on the ground will be well hidden in the grass).
Besides, Lucy approaching for CQC is an absolute certainty considering the previous point of no objects to throw and her nature as that option is more in character for her. And when you consider this point with Jotaro's first impressions, him being oblivious to her vector's powers and the fact that he has one of the most powerful stands in the world, why would he not accept Lucy's CQC invitation (her approaching him)? He wouldn't see the need to go for the trouble of finding a projectile to OHKO someone when he can just approach and accomplish the same results but with seemingly lesser difficulty and effort (which despite not knowing he can OHKO, he will). Though, I have to acknowledge that when he approaches and he's likely to do it for the previous reasons, he will do so attentively.
But, here's something that I should've brought up before but didn't for not thinking straight: Lucy needs to activate her vectors on her own accord. If she doesn't activate them, Jotaro can't see them. The same goes for Jotaro summoning SP: he doesn't summon him, Lucy can't see him. The big factor here is that when Lucy approaches him, she won't activate her vectors yet, considering she only activates them to hurt/kill opponents in her range, throw projectiles against opponents out of her range or to defend from incoming projectiles. But none of those are true while she approaches Jotaro in this scenario. Ergo, she won't summon them yet because she has no reason to just yet.
She'll summon them the moment Jotaro is in range and, just so you know, she has a good sense of how long her own vectors are. Now, you might think that when she's exactly 11m away from Jotaro she'll summon them. But then remember, she doesn't rely on having a keen calculation sense: she relies on intuition (meaning she'll summon them when she feels that she's close enough). And also, she's cunning like him!~
All this means that she could summon her vectors at even shorter distances than 11m (though she'll still keep her distance). And considering her naturally bloodlusted nature and cunning, the probability of her summoning her vectors at shorter distances than 11m will be pretty favorable. And in case you doubt she's clever enough to do that,
here we have her tricking a guard to steal his key and escape in the manga , and this was at the very beginning of the manga. I can provide more intelligence feats for Lucy if needed.
And when she does this (and it's likely she will), this will most likely cause Jotaro to stop on his track and decide to back out from CQC when he sees the vectors swarming him (considering they appear from thin air fairly quickly). Depending on the distance she summons them, two things can happen:
1. If she summons them below 10m, Jotaro tries to get away, but due to being too close (and Lucy likely getting the jump on him) still gets caught by Lucy's vectors, and then she kills him by negating durability and ripping his heart out, brains out, breaking his blood vessels, etc. He can't focus on trying to OHKO Lucy or doing anything else due to being swarmed and unable to shake off her vectors. SP can, but Jotaro can't (28 limbs vs 4 limbs)
2. If she summons them 11m or above, Jotaro successfully gets away and starts relying on his surroundings to kill Lucy, which considering he's clever enough to come up with ways, he should be able to pull something off. But he'll have troubles with Lucy's better mobility.
When you consider the previously mentioned factors, the former scenario is more likely to happen with a decisive victory for Lucy. But in the latter case (despite being unlikely, CAN happen), Jotaro has better chances of attaining victory than Lucy as he's more clever than her, but less mobile (about 55-45).
To sum up, Lucy's better starting mentality (bloodlusted nature) will allow her to make the best out of her advantages (range, hax, mobility) and common strengths (cunning and durability negation), and use them cleverly enough to kill Jotaro before he gets the chance to fully utilize his advantages and common strengths more often than not.
And with this, I cast my vote for Lucy.
I'm gonna go get me some lunch.