Scaling is not the same as normalization. You have empirically discovered how scaling affects PCA, and it's purpose is to control whether large peaks dominate the analysis or not.
Normalization on the other hand is typically done when samples were in a solvent and the concentration could vary due to the extraction method, the hydration of the tissues etc. So normalization tries to compensate for these varying concentrations.
Normalization would normally be applied across the peak intensity vs time dimension. Two typical normalization schemes are 1) normalization to constant sum (usually 1) and 2) Probabalistic Quotient Normalization which uses a slightly more complex approach (and is frequently preferred). I don't work with LC-MS data, there may be other methods that are preferred with this type of data. Whatever software you are using probably has several options built-in.
Probabalistic Quotient Normalization is reported in F. Dieterle et. al. Analytical Chemistry vol. 78 pages 4281-4290 (2006). The exact same mathematics are called "median fold change normalization" by Nicholson's group, reported in K. A. Veselkov et. al. Analytical Chemistry vol. 83 pages 5864-5872 (2011).