I am glad that you made it on time. Congratulations! Happy for youI don't know if this will help to clarify the situation because like mom told me it's like rolling a dice . But I'll put what am sure of and what I learned from my own experience.
When I got selected i didn't think that pending asylum will be an issue but turns out you have to fit a criteria so you can adjust your status while pending asylum.
as we all know to go through AOS as DV lottery you have to be got selected , their is visa available for you at the time plus been admissible.
what i learned is if applied for asylum within one year from states entery was in a valid visa status which you didn't violate your visa category and was inspected and paroled in the border while entering the states. That all means you didn't accumulate any unlawful stay according to the exception in INA 212 under unlawful presence here in fact you are in a lawful stay which make you admissible to states under other categories like dv lottery or getting married if the officer reviewed your asylum case an determined it's not fraudulent.
With that been said that my knowledge that I gathered thro search speaking to a lawyer during my RFE which they asked for my school records to determined the time line about my entry and when I applied for asylum and if i did attended and finished my school while also I didn't break any law about my visa like worked while I was student without having any work permit.
I also spoke with cpl ppl personally went thro this which they didn't have a problem with this issue unfortunately one of them didn't get it for other reasons which is visa availability at the time.
My IO also made sure that is not a problem after he went thro the documents in this topic in fact I asked him what should I do if I got approved should I withdraw the other case he said that well it will be canceled automatically but it's not bad to do so as well but you have to wait until you get the card in hand . note he didn't approve my case at the moment because he was waiting for my asylum case..
I tried to make it short as possible i think it still kinda a gray area for mom ask me anything so if I forget something I might remember a point that is important.