Q. Does one say Keil Erech Apayim before Krias HaTorah on Mondays & Thursdays only on days when Tachanun is said, or is there no such connection and it should always be said?

A. According to most Poskim Kel Erech Appaim follows the saying of Lamenatzeach and is recited even when no tachanun is said ((See Remo O.H. 131: 1, Shulachan Aruch Horav 129: 12,, Chayei Adam 32: 34, Kitzur S. A. 25: 2, et. al.).
Some maintain That in the days you do not say tachanun you also omit Kel Erech Apayim (Shiurei Knesses Hagedola 131, Pri Chodosh ibid. 1, Siddur Hattania, Shulchan Hatohor 131: 19, et al.).
Horav Shlomo Miller’s Shlit”a opinion is that one should follow the nusach of the congregation where he davens.

Rabbi A. Bartfeld as revised by Horav Shlomo Miller Shlit”a