WOW I was surprised no one responded.
Your question is a compound question:
1.) Can you use invert sugar to bottle? Yes I have never done so, but the yeasts can consume both the monosaccarides in invert sugar just fine.
2.) Can you invert sugar in a wort boil? No absolutely not. "Boiling temperatures in the range 225 deg F to 300 deg F are high enough to cause significant inversion." http://www.allbusiness.com/wholesale-trade/merchant-wholesalers-nondurable/721156-1.html
3.) Does the acid ( lemon juice) work to break the sugar down? No. The acid has very little to do with that (nothing at all really). The acid whether it's lemon juice, cream of tartar or vinegar only serves to interfere with crystal formation while the sugar is being heated.
Invert Sugar (what I suspect you are referring to) is Sucrose that’s been through hydrolysis. In hydrolysis the disaccharide is broken into down leaving the two sugars glucose & fructose. When you do it the process requires enormous heat. When a yeast does it they do it so very elegantly using enzymes to coax the bonds apart.
You can not invert sugar in a wort boil.
This is because you can not achieve the heat necessary to break the molecule in a 212 F boil.
That's what happens when you invert sugar: you break the bond using heat. The result is two monosaccarides ( glucose and fructose) the reason an acid is used is because you need something to interfere with crystallization. Cream of Tartar, vinegar and lemon juice are all used variously. I don't know whether one is better than another or even if one is more suited to some end use over another.
As a general proposition wort will have 5 sugars They are glucose, fructose, sucrose, maltose and maltotriose.
Interestingly the yeast use these sugars in a linear progression consuming
Glucose first, then fructose, then sucrose, then maltose with maltotriose being consumed last.
Sucrose is, as you know, made up of glucose and fructose. When a yeast cell encounters sucrose it takes it into the cellular wall where the sugar is broken down (hydrolysed) using the enzyme invertase. The result is glucose and fructose
By using invert sugar you will have already done this work for the yeast.
It is interesting how much energy you had to put into the sucrose to invert it but how little the yeast does - yes? The yeast enzyme process is far more efficient.
Once the Sucrose is broken down the fructose and glucose are assimilated into the glycolytic pathway (http://biotech.icmb.utexas.edu/glycolysis/pathway.html ).
Maltase is the enzyme that carries maltose and maltotriose through the cellular wall. Maltase is blocked by the monosaccarides glucose and fructose. So until those have passed through the wall and been consumed the maltose and maltotriose are left outside which is why they are consumed later.
As an after thought you mentioned adding the sugar to the boil.
If you did this, then no matter what sugar you used it would be consumed in the ferment up to that point where the alcohol killed off the yeast. You'd have a very alcoholic brew around 10% I should think. Then, to bottle carbonate, you'd need to pitch a more alcohol tolerant yeast like a champagne or wine yeast along with the extra sugar ( assuming there was no sugar left in the original ferment) . Which parenthetical causes one to wonder whether there would be a way to accurately gauge the amount of sugar you have at bottling. You would need to use a hydrometer to measure the sugars remaining as compared to what you started out with
(way too sophisticated for me as I use the Trappist "suck-on-the-finger" test). I'd guess they'd be maltose and maltotriose that would remain but that would depend on how much invert sugar you added to the boil to begin with.