probably borrowed from German Alexie, from a-a- entry 2 + Greek léxis "speech, word, phrase" + German -ie-ia entry 1 — more at lexis
German Alexie was used by the Austrian neurologist Moritz Benedikt (1835-1920) in "Ueber Aphasie, Agraphie und verwandte pathologische Zustände," Wiener medizinische Zeitschrift (6. Jahrgang, Nr. 48, November 26, 1865, pp. 1167-69), though it is not evident that Benedikt coined the word. It is clearly modeled on Aphasieaphasia and Agraphieagraphia, but Greek léxis, derived from légein "to speak," does not pertain to reading; Benedikt (if he coined the word) may have confused léxis with derivatives of Latin legere "to read," as lēctiō "act of reading" (cf. lection).