I wouldn't heat up the honey... If it's liquid, just mix it in...
This is going to be a 'cold' project...
I would taste the lemonade before going with this. If it's sweet, you could start on the low end of the honey range. You could use good sugar to (dememera comes to mind) instead of honey, if you wish... Or combine both... Since it's carbonated, you might want to let it go flat, then take a hydrometer reading off of it...
1 pound of honey will increase the must gravity by ~7 points, in 5 gallons of solution (total)... 12 pounds of honey typically takes up 1 gallon of volume...
So, if the stuff you have in bottles tastes decent/good, use it. If it's butt-nasty then toss it... Or make a small batch, to get your feet wet, and reserve the rest for a bigger one.
I would get a hydrometer as soon as possible... It's a critical tool to have when you're brewing/fermenting anything. Without it, you won't know what you have for potential, or when things are really done...
DAP is a yeast nutrient... You could also boil up some bakers yeast, to use in place... Typically with mead, and high OG must/wort, you'll want to give the yeast nutrients to help them along... More important with must (which is what you'll be making here)...
Slight stab in the dark without knowing the gravity of the lemonade... But tasting will tell you about how much sugars it appears to have... Assuming it's medium sweetness/dryness I'd say it's probably about 1.015 (complete stab in the dark though)... If you use 4 gallons worth of the lemonade, I would still go for 6-10 pounds of honey... Make one, see how it is in 4-6 weeks, and then alter for the second batch...
DO get a hydrometer though... If you can get one before you start this, it will be a HUGE help... Without knowing the gravity of the lemonade, it makes things more difficult... With a hydrometer, you could also use the Dememera sugar to get the OG to where it will make something strong...
I would aerate the crap out of the must before you pitch the yeast in. I would also make a starter for the yeast... You can do that with a weaker must, say a few ounces of honey in a quart of water... Once it's fermented that, add a few more ounces of honey... Let that go, and see how much yeast you have in the container... I would use DAP or even the Wyeast Beer Nutrient to help things along... While yeast loves sugars, it needs other things to really do well... That's what the nutrient will provide.
How strong would you like this to be? That will really determine how much sugar/honey to use... Plus, how much sugars are in the lemonade...
I'm planning on making mine in the 6-12% ABV range... Probably looking to use 1.5-3 pounds of honey per gallon of must... You can use the
mead calculator to get a base mead ratio/recipe.. Assume very little gravity contribution from the lemonade, look at it as more of a flavor element...
Hope this helps, and doesn't make it more confusing for you... If you have time (which you probably do) make a test batch, or one batch first... You can always tweak the second batch to get something different from it all... Either way, you should get something good (provided the lemonade is good) out of this... Make one batch strong, the other modest, and mix them up when you give them to your friends...