gonna spoon feed.
learn to read the laundry symbols on your tags. the vast majority of lolita can be hand washed or dry cleaned, and some modern pieces can even be machine washed (generally turned inside out, in a bag, with detachables removed, cold water gentle cycle).
-anything post 2010 probably won't give you much trouble. worst cases being cotton pieces with reds or blacks, and certain prints. but spot check a waist tie or something if you're that scared
-most cotton can be dry cleaned, again check the tag
-cold water, mild detergent. oxy works on a lot of things, but is best avoided on bleed-prone stuff
-don't soak it, and when you're done washing, roll it into a towel and press as much water out as possible. the less time it spends wet, the less bleed you'll deal with.
-color catch sheets. they even work with hand washing.
if bleed does happen, it can sometimes be washed out, spot cleaned, or otherwise. using a dryer can set the dye, which is why hang and flat drying is best.
-if it's real velvet, dry clean or gentle hand wash. if it's a poly velvet it shouldn't be particularly fragile, again check the tag.
-steam, don't iron
-don't be aggressive when scrubbing
leaving your pieces dirty leaves your skin oils in the fabric, which can stain and degrade the fabric and cause damage.
tldr: lolita isn't hard to clean, you are just either lazy, or misinformed by outdated blog posts on the topic.