Sterilize your jars. Put the lemon slice in the bottom and pack the trimmed and blanched asparagus into the jars (it’s up to you to determine whether you want to go tips up or down). Tuck a garlic clove down into the asparagus spears.
Bring the vinegar, water and spices to a boil. Pour into jars on top of asparagus, leaving at least 1/2 inch of head space.
Put lids and rings on the jars and process in a hot water bath for 10 minutes (you can skip this step if you plan on just putting your pickles in the fridge).
Wait at least 24 hours before eating, to give the asparagus spears a chance to get sufficiently pickly.