I think it was either a manhwa or manga, where the MC was living inside some kind of mansion / a wealthy person's house (I'm not sure if he was a slave, hostage, or etc, all I know is that he wasn't treated fairly by the people in there) and then met the ML and begged the ML to take him along with him and get out of that mansion. The way MC begged wasn't really the miserable way of begging but more like "Please take me with you bcs I can't stand these people!", the more confident / bargaining type if you will
That's all I could remember...
Nvm already found it, it's "My Refuge" (I'm shit at remembering things if you can't tell ) https://www.mangago.me/read-manga/my_refuge/

So for some reason if you search "Lullaby of the Dawn" the manga itself doesn't come up, you gotta search "Yoake no Uta." Just letting you know (because it took me like an hour to figure it out lmao)
thanks for the tip pookie
imma read this bc u took one hour to just figure it out