What is the teaching in choosing lemons—I know the obvious of picking heavy weight lemons, avoiding a dried-out looking lemon with significant pitting. I was reading that one must choose thin-skinned lemons but how would u know that without cutting the fruit? Any other recommendations for getting lemons with a bright, lemony, flavor without so much bitterness? 
No. There are so many products used in so many different ways in crop protection and as preservatives for harvested fruit, that it is impossible to say beforehand what the most likely contaminants are and how to test for them. I was hoping only waxed fruit is treated with preservatives, and that i could test for wax easily, but it is impossible to say if a lemon was waxed, and unwaxed lemons may be contaminated also. I have not even been able to find a top 10 list of most-often found pesticides and preservatives on/in lemons. The name that does come up very often as a preservative applied after the harvest is Imazalil. The up-side is, it can be washed off to some extent. But this only focuses on the zest, and unfortunately 1/5 of Spanish lemons (and 1/2 of the Turkish) contain chlorpyrifos, which is neurtoxic pesticide that will be banned at the end of this year (2020). It is added to the ground so it is in the fruit, not just on it. In general however most of the preservatives and pesticides stay within safe margins (Dutch link). If the farm also sells to supermarkets and such the product will have to be clean enough to pass tests, which most fruit does. I have found little info about what organic farmers use to protect their crops, what i found seems pretty ok (Dutch link). Also the lemons are in season currently so they are anyway less likely to be treated after harvest. The best options are to contact the farm and decide how much to trust them or to rely on store-bought food that has some labelling and certification. 