roasted garlic probably would be great, but i've only made from raw, more like a tsatsiki sauce. the raw garlic is chopped and scraped into a wet mush with a chef's knife and a bit of medium sea or kosher salt. or you can use a mortar and pestle, starting by grinding dried chipoltes, then raw garic.
for the lemon and thyme, i add zest and a bit of sugar. use meyer lemons if you can get them.
A true lover of nature does not despair now that his mistress has turned a colder cheek.