It may be looked down upon but it might be possible, since we do not get any 360 view of the gems, Fusion is looked down by homeworld but it isn't really, Fusion of two different kinds are looked down by homeworld they view it as disgusting, As said in an Episode on Steven Bomb 4.
And also I have noticed that Lapis Lazuli said "Do you even know who I used to be?" which may be also a information that She was a fusion of Blue Diamond but was trapped in the mirror, You can also see the Paintings or Carving in one of this image.
Which might be the past "Diamonds" exception of Yellow Diamond since you see the image shown has no Gem in her forehead which might be another clue, Saying that Lapiz Lazuli was a fusion of the same kind of gem/class.
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I don't think Lapis is/was Blue Diamond but I definitely think she was a high classed gem. Obviously gems that are rare/powerful have high class in Homeworld, and Lapis is shown to be very powerful. However, this may not be true as water may be non existent on Homeworld (shown in When It Rains where Peridot is unfamiliar with rain).
I guess White Diamond could be a fusion of the same kind of gem but I don't think that really makes sense in terms of the gem hierarchy. If that was the case then they could just fuse a bunch of Jaspers together and make a super powerful Jasper and call her 'Orange Diamond'.