Ultraman Leo song "Hoshizora no Ballad" (from the mid 1970s)
And this is the tune we were listening to - Ys IV : Mask of the Sun - song "I Want to Be Gentle" (well, that's what YouTube calls it)
(NB: YouTube timed embed code appears to be a little dodgy, wait a few seconds for the song to start, or manually skip to 51:34)
Or, the nice FM oscillator / PC Engine version of the same Ys IV tune (also available on Amazon!):
Very similar, eh? Don't know whether this is the same composer, or based on the same folk tune or lullaby or something.... or a happy coincidence or it's just plain old plagiarism. Very similar, though!