It is, yes. The story order has altered but will remain more or less the same, she'll relive the beginning sequence after beating the Lady of the Lake.
speaking of... where is lady of the lake, i did the lantern skip and the normal route and found nothing but walls. The lantern pogo was really fun though.
Looking forwards to remastered dragon robot guy and Lady of The Lake, both the OGs were really good fights that had a lot of further potential, I feel like Lady of the Lake needed a better ranged move, but was really good other than that.