So unfortunately, after buying the LG G4 and downgrading it to Android 5, it gives me eye strain.... I checked the stats and it uses newer graphics card than my lumia Adreno 418. So I think I am sensitive to something what comes from this graphic card. Will have to sell it because the phone comes sealed and once the seal removed it is impossible to return (the seller told me I will be able to return...).
So next step for me is Oneplus X. I checked the stats - they are the same as my beloved lumia (Adreno 330, amoled screen, Qualcomm Snapdragon processor) and it comes with Android 5. It is also easy to flash this phone so if it turns out to be good for my eyes I will try android 6/7 and even 8.
During the last days I also checked couple of Samsung phones - A8 (2018), S6 EDGE PLUS, S7 (all Android 7 or 7.1). All give eye strain, blurry vision and some dizziness.