There's an obvious similarity between the Proto-Indo-European reconstructed roots *leg- and *les-, both "to collect, gather", reflected in logos, Latin lego and German lesen respectively. I have not yet seen a comparison of the roots, and did not research explicitly, other than looking up Wiktionary.
I am hoping someone knows a reference from the top of their head.
I see three possibilities:
There is a common root to the two reconstructions and a grammatical explanation for the dissimalirity.
1.a) lesen did not have the connotation of reading. The sense is a phono-semantic loan from a christian incurser.
1.b) "lesen" had the connotation to pick up hints for long.
Both roots were the same but at different stages; Which would imply sound change not shared by both branches as early as in a PIE dialect scenario or at the latest in a scenario in which noble savage learns to read from forreigners--similar to 1.a)--and borrows the whole word mutating it slightly (Galician lesen, 3rd p. pl. subjunctive participle of ler "to read" < legere, reminds of Ger belesen "learned")
I'm sure that there is no main-stream hypothesis, otherwise I'd expect Wiktionary to note that. I'm pretty sure there are at best non-comittal opinions or unacceptable fringe theories at worst about questions concerning the timeline of PIE and unproven sound-changes. I think it is impossible to give an acceptable negative answer
I'd be surprised if a tentative synchronic explanation has been given on the example of exactly these two roots. A general grammatic theory to synthesize an answer would probably be beyond me; I expect I will not find the answer in introductory text-books (if that constitutes lack of prior research, the question should be closed, or put on hold for a long while).
So i guess I'm asking: Have I missed another principle possibility?
This could be deemed to broad and unlikely to result in a high quality answer and more likely to result in a low effort answer about the uncertainties of etymology, which would be yet too much effort to ask, for what it's worth, on the basis of the question.
What I really want to know is actually:
Is there a theory for a root *le-?-? Ideally, that should explain a few other *l- initial roots as well, perhaps even glossa.