How exactly are you opening your files in Fiji? File > Open?
I’m asking this ‘silly’ question because there are in fact multiple ways to open image files. If working with .lsm files, I’d recommend opening your images via Bio-Formats (File > Import > Bio-Formats). This would be one thing to quickly test if you haven’t used it yet.
In any case - the color is relatively un-important (or at least it can be changed as you want/need), as it is only a pseudocolor image and a new LUT can be applied at any time (the Visualization page has some helpful stuff in there). The most important thing is that your channel order is consistent - so selecting the correct channel is not affected.
What are you next steps for processing? You can write a script too to be sure to set the channel colors as you’d like for each image, etc.