I assume that your letters are rendered on a transparent background. I think this s just a programming issue...

Cue 1 - Fade up layer 1 (A)
Cue 2 - Fade up layer 2 (B) - [layer 1 is still at FULL from cue 1]
Cue 3 - Fade up layer 3 (C) - [layer 1+2 are still at FULL from cue 1+2]

There are no cross-fades - but you do use 3 layers

Diples crossfading is a function of most lighting desks - but most dont do it very well as most lightsources dim in different ways!- try changing the xfade curve in your cue on the lighting desk, or delay the fade out cue slightly

If you have a lot of letters (ie a sentance) then you should make a movie file with the correct fading (building). Then you can play this on 1 layer and just play between the 'in' and 'out' points if each letter needs to be cued. (else, just let the movie runif your timing is correct in the edit)

A number of video editing softwares have text tools built in, so it would be fairly simple to create.

Simon