“Le’avdiacha”. Rav SR Hirsch explains the root /ayin-beis-dalet/ as a more intensive form of /aleph-beis-dalet/, to be lost (just as an ayin is like an alef, but is supposed to be voiced). To lose one’s goals to another’s', working entirely for another person. Here we speak of taharah from inappropriate goals so that one can work entirely toward the aims Hashem spelled out for us.
I would think that a Ba’al Mussar would focus on “vetaheir libeinu”, while the Chassid would read them as secondary to the next — le’avdikha. True to the fork in the hashkafic road between Litta’s focus on sheleimus, wholeness and completion, and Chassidus’s focus on deveiqus, cleaving to G-d.
Bi’emes — in/through truth: At first I took this to be an adverb for le’avdekha. However, I want to draw attention back to the first thing I skipped in this quote, the opening letter, “vav — vetaheir”. It begins with a prefix meaning “and”. This makes our phrase part of a list, along with, “qadsheinu bemitzvosekha, vesein chelqeinu beSorasekha, sab’einu mituvekha, vesamcheinu biyshu’asekha”. In all of those cases, the noun at the end of the phrase is the means by which we ask for the thing described by the rest of the phrase; for example “Sanctify us through your mitzvos”. (The mem in “mituvekha” deserves comment. Another time.) So, here too, emes would be the means, not a modifier for le’vadekha.
Taking the phrase all together: We are asking for Hashem to give us emes, by which we will get the taharas haleiv necessary to answer only one calling — His.