I'm positive you're right about his definition of lover being something else. I think he sees him as his own grandpa because he was a lonely kid and Shigekazu-san was the only nice and loving person he had (probably). As I see it, there's no romantic undertone between them, even if Mitsuki uses the word 'lover', it would be one sided on his part because the grandpa never actually agrees and the fact that he doesn't correct Mitsuki is just for the sake of mistery lol But it's a funny setting tbh
well he said himself " i wonder if i become a lover will someone sta with me" so i'm pretty sure he just wanted someone to be with him cause he was lonely and as a kid he didn't understand the meaning + the grandpa kept it cause he was a kid and he found it cute so it stayed as a game. IF it was THAT kind of manga i'm pretty sure that we would have noticed it already xDD
Well, I don't know haha All of that was sweet and cute but I still hope that their "love" is/was platonic, or the kid's definition of "lover" was something else. I understand that age is just a number and all that stuff (duh), but come oooon he was a kid at that time, a kid! Age gap is just too big!