Wash okra well. Trim by paring away all but about ¼ inch of stems and removing the skinny leaves that surround the crowns. With a sharp paring knife, poke 3 or 4 holes in each okra pod to help the brine soak in.
Divide jalapeños, lemon slices, and spice among warm, prepared jars. Keeping the 1-inch headspace in mind, pack okra into jars, alternating tail end up and down, until they fill each jar snugly. The okra should not poke up over the headspace and any that do should be trimmed again.
In a 3-quart saucepan, bring vinegar, water, salt, and garlic to a boil. Pour hot brine over okra, adding one garlic clove to each jar and leaving 1 inch of headspace. Give it a minute or two to settle, then add more brine, using a chopstick or plastic knife to settle okra back into jars. Continue to add more brine, remove air bubbles, and allow okra to absorb the brine before reviewing the headspace. During processing and as the pickles brine, they will absorb liquid. Adding as much liquid as possible now is the goal, but maintaining headspace is also important. This takes practice.
Clean rims of jars with a damp paper towel. Place lids and rings on jars and finger-tighten the rings. Process in a boiling water bath for 15 minutes. Let the jars sit in canner for 5 minutes to prevent siphoning. Let pickles cure in a dark, cool space for 1 month before eating.