Prepare a boiling water bath canner and three half pint jars.
Combine the tomatoes, sugar, vinegar, jalapeños, salt, and lemon zest and juice in a low, wide, non-reactive pan.
Bring to a boil over high heat and then reduce the heat to medium. Simmer until thick (30-45 minutes, depending on the height of the heat and the width of your pan).
Use an immersion blender to puree the jam a bit, if you want a smoother texture (this also helps integrate the jalapeños, making for a more uniformly spicy preserve).
Funnel into the prepared jars. Wipe the rims, apply the lids and rings, and process in a boiling water bath canner for 15 minutes.
When the time is up, remove the jars and set them on a folded kitchen towel to cool. When the jars have cooled enough that you can comfortably handle them, check the seals. Sealed jars can be stored at room temperature for up to a year. Any unsealed jars should be refrigerated and used promptly.