In a large pot, combine the lemons, apples, red peppers, jalapeños, salt, sugar, and vinegar. Bring to a boil over medium–high heat. Reduce heat and simmer, stirring often and reducing the heat as necessary, until thick. Remove from heat and fish out the lemons, which will now just be soft pieces of peel; discard lemons.
Ladle jam into the hot jars to within ¼ inch of the rim. Remove any air bubbles and wipe rims. Place the lids on the jars and screw the bands on until fingertip-tight. Process in a boiling water canner for 10 minutes.
Notes
This jam is quite vinegary in taste but make sure to boil it sufficiently, not only to thicken it but also to mellow out that vinegar taste. Acetic acid is quite volatile and so boiling will cause some of that to evaporate.
For this jam to set, you need to boil it to the jam set point, at 220 °F (114–115 °C) at sea level. I've found with some batches, boiling up to the set point can even result in a fully gelled preserve, much like a pepper jelly and without having added any extra commercial pectin!
For a spicier jam, use less Bell peppers and use more jalapeños. Just make sure that the total weight of peppers is the same (~700 grams). You can also opt to incorporate spicier peppers in the mixture, but be careful as some hot peppers are quite spicy and too many may make the level of heat unbearable for some people.
If you find your yield is much higher than the yield in the recipe (meaning you end up with more jars of jam than expected), it could be that you didn't boil the jam for long enough. The set may also be more loose because there is more water in it.