The relevant info:
Mycosynth Lattice

Artifact
All permanents are artifacts in addition to their other types.
All cards that aren't in play, spells, and permanents are colorless.
Players may spend mana as though it were mana of any color.
Pentad Prism

Artifact
Sunburst (This comes into play with a charge counter on it for each color of mana used to pay its cost.)
Remove a charge counter from Pentad Prism: Add one mana of any color to your mana pool.
502.37a Sunburst is a static ability that functions as a spell is resolving. "Sunburst" means "If this spell is a creature spell, it comes into play with a +1/+1 counter on it for each color of mana used to pay its cost. If this spell is a noncreature spell, it comes into play with a charge counter on it for each color of mana used to pay its cost."
502.37b Sunburst applies only as the spell is resolving and only if one or more colored mana was paid for its costs. Mana paid for additional or alternative costs applies.
I believe (but am not 100% sure) that using mana
as any color mana is not the same thing as
actually paying the Prism's casting cost with colored mana, so if you want to get full use out of a Pentad Prism, you have to pay for it with two colors of mana, even with Mycosynth Lattice in play.
In other words: sunburst goes to check what kind of mana you
actually used, and not what it was used
as.