Wallpaper help

I cross lined my walls before papering and the guide I used said to leave a small gap between pieces. I then wallpapered over the top and it looked fine for a week or so. Now the paper has shrunk into the small gaps in the lining paper.

Is there anything I can do about this without removing the paper?

Nope unless you want to strip the lot off and start again.The lining paper gaps must of been quite big for them to show through the finished paper.Sorry not what you want to hear but I cant think of an easy solution

The gaps were very small when I put the paper up, it's almost like the lining paper has shrunk after I put the top layer up.

There shouldn't really be any gaps, but when lining if there are , these can be filled with a fine filler prior to putting you finishing wallpaper on.
As mentioned there isn't really any way of solving it other than starting again.

When doing my apprenticeship, I was always told to leave a 1mm gap and nothing more when cross lining and, as suggested in the original post, many lining paper instructions and guides would also recommend it. (Although that doesn't seem to be the case these days.) The reasoning, I was taught, was that the 1mm gap allowed for any further slight expansion of the lining paper when the wet finishing paper was hung on top of it, thus eliminating any ridges in the finished surface. It makes sense and a 1mm gap would never cause any issues, although many other decorators would always butt the joins tightly.

With the differing types and qualities of lining paper available now, it is wiser to use a non-woven one (which don't expand or contract) and butt the joins together to avoid the issue you have encountered.

Unfortunately, as already mentioned, there isn't much that can be done to resolve the problem now, other than start all over again.