Mellifleur

The being called "Melif" in the 3e Manual of the Planes appeared in 2nd edition's Monster Mythology as Mellifleur.

The Manual of the Planes doesn't mention that he's a god
because there was some kind of prohibition at the time against
mentioning gods that weren't in the PH or MM. That's why, for example,
Clangeddin is called a "dwarven hero" instead of the intermediate deity
he is, why the Norse god Loki is only called the Trickster, and why it
doesn't mention that the Teardrop Palace in Gehenna is ruled by the
Chinese god Sung Chiang.

The connection between Mellifleur and Bane was something created by Carl Sargent in Monster Mythology.
He wasn't a Forgotten Realms guy - he was the Greyhawk guy - so perhaps
it should be taken with a grain of salt. The name Bane was just thrown
out there, not put in because it was a fundamental part of the concept,
or due to any great deliberation.

The myth in Monster Mythology went like this: Mellifleur
was an ancient wizard who wanted to be a lich, but due to a freak
coincidence an evil deity - variously named as Nerull or Bane,
depending on the world - was trying to raise a servant to divinity at
the exact same time, and the energy went to Mellifleur himself. So he
became both a god and a lich simultaneously.

Here's the catch: illithids, who tend to know what they're talking
about and have little reason to disseminate spurious myths about gods
they don't even worship, have a variant version of the story that says
that a number of evil deities on a bunch of different worlds were all
trying to raise their own servants to divinity at exactly the same
time. So Nerull, Bane, possibly other gods like Chemosh and Azrai were
all initiating prospective godlings simultaneously. Because of this,
Mellifleur went directly from a nobody to a lesser deity instantly. He moved to Gehenna and now Nerull and other evil deities are
after his throat for "stealing" the divine ranks they meant to
invest in their own servants. Even though he's evil, he thus has to
oppose those other evil deities. He also opposes Cegilune, queen of
the
Night Hags, because he needs the Larvae they harvest to sustain
his
power. The Altraloth Typhus was created by the night hags to
defeat his armies.

Velsharoon was connected to him later on, in Powers & Pantheons. So maybe it wasn't Bane,
maybe it was Talos, and maybe what really happened was Nerull was
trying to deify Kyuss and Talos was trying to deify Velsharoon, and
maybe this happened millennia apart, but somehow the planar-temporal
wires got crossed and Mellifleur was an unexpected byproduct, getting
some of their power. So maybe Mellifleur has to oppose not only Nerull
and Talos, but also Velsharoon and Kyuss, too.

Or maybe Bane was involved, but not on Toril. Maybe it was Bane on some other world where Bane is worshiped.

The stories of Velsharoon and Mellifleur have some parallels, of
course. Both became gods and liches simultaneously, and both pulled the
wool over the eyes of evil deities, Mellifleur accidently and
Velsharoon on purpose by letting Talos empower him just before
switching allegiance to Mystra. Both have to oppose the schemes of the
gods who gave them birth.

Maybe in some way, cosmically, they're the same, but Mellifleur's origin is tied to many worlds and Velsharoon just to the one.

Sources:

Manual of the Planes (D&D 3.0)
Monster Mythology
Powers & Pantheons (Velsharoon)
Faiths and Pantheons (Velsharoon)