I vaguely remember the premise. It's about a woodcutter/mechanic that took care of an injured Asian type dragon. It's set in an alternate historical Japan. That woodcutter is a bit old, around 30s. And the dragon can transform at will, and is pretty young. The dragon fell in love, of course.

I remember that the dragon' dad eventually came down to visit to judge the woodcutter.

And that's all I remember. I THINK, the dragon knew the woodcutter before he was even injured, but I'm not positive.

Possibly Tatsu no Otoshigo?

⇢⋆⇠⇢⋆⇠⇢⋆⇠⇢⋆⇠⇢⋆⇠⇢⋆⇠⇢⋆⇠⇢⋆⇠⇢⋆⇠⇢⋆⇠⇢⋆⇠⇢⋆⇠⇢⋆⇠⇢⋆⇠⇢⋆⇠⇢⋆⇠⇢⋆⇠

Moved to Yaoi/Yuri.

YES! It's this one!! Thank you!!