Sizing is normally much thinner than the mix required for lining paper (which, yes falls under the normal paper category).
To be honest, I normally mix 7L per sachet of Solvite as per the instructions for "normal" paper when lining walls. I then use the same mix to "size" the walls and then apply the same mix to the paper. I hang the lining paper whilst that section of wall is still wet. Doing so means that I am guaranteed that, on hot days, I do not need to worry about any dry spots.
I completely understand you not wanting to bin the stuff you have already mixed but buying more paste will be cheaper than potentially having to deal with problems with seams further down the line.
It may be the case that you will get away with doing a wet on wet coat- ie pasting each section of the wall as you apply the freshly pasted lining paper but that that may require you to purchase another sachet of paste anyway.
Oh, and resist any temptation to sprinkle a bit more paste powder into the current mix- it will go lumpy. There is an outside chance that you might be able to make a thick mix and blend it with your current mix, but again, it may become lumpy. Wall paper paste is a relatively cheap product. Per square metre coverage, lining paper and paints, or top cover wall papers are far more expensive.
