The mushrooms all spawn in the same places in the Bramblewood, they don't have separate locations for different types. If you have Seasons they don't all spawn in all seasons though. Lovely mushrooms only spawn in Spring and Fall, iirc.
It is deceptive because most of the rest are "all seasons" but the lovely ones are not. The Nightly mushrooms are also not all season, they are Winter (and nighttime) only. Just in case that ever comes up for you as well.
If it's not the right season and you want to try to get some sooner than the season change, you can also get them as gifts from wild rabbits and birds...though that is so random it's not something you can count on.