It is possible to use basal only as you are relatively newly diagnosed so still in the honeymoon period. But it depends.
Do you see significant spikes after eating? Do your levels return to a stable lower level?
I have not used Lyumjev. I use Fiasp another faster fast acting insulin. My experience is that the speed is dependent upon my BG when I inject. If my levels are above 10, it can take getting on for an hour to start working. If my levels are in the 4s, it will work immediately. If my levels are between 5 and 8, i takes about 15 to 20 minutes to work.
Bolus timing attempts to match the peak of the insulin activity profile to match the peak of the carb digestion profile. Different food has different peaks. We use fast acting carbs for hypo treatment because their peak is very soon after eating. On the other hand, high carb high fat foods llike pizza can peak much later: I find my BG could continue rising for 4 hours after a pizza.
All of this is building up to explaining how the peak of Lyumjev may be earlier that the peak of your carb digestion which leads to the hypo. If this is the case, taking your insulin later will stop the hypo. If my BG is in the 4s, I take my Fiasp after eating.