To start with...Unless the vehicle has a SS paint system, you will not be applying an LSP to 'white paint'. Instead, an LSP will be applied to a non-pigmented clear-coat, which is the top-coat paint-film of a BC/CC paint system.
Now...Once the CC paint-film, of a BC/CC paint system, has been properly detailed (such as: washed; decontaminated; clayed; polished) to meet the expected standards set forth by, and of, the detailer...It (the CC paint film) will then be at one of its most glossiest/reflective/shiniest moments. This 'corrected' CC paint film will then allow the truest hue of the BC's color to "shine through"...(And since we're on the subject)...Even if it happens to be a white, or most other light-colored, BC paint films.
Another thing to keep in mind is the color spectrum, how colors are "made", and how it is even possible for us human beings to actually see color(s).
A good rule of thumb I go by is: Along with the 'corrected-CC' reflecting light, the now exceptionally-well, shining-through-the-CC, BC white colors will also reflect light
without absorbing any of the color spectrum...The results being a top-coat paint-film surface usually exhibiting a glossy, bright, yet 'flat' shine...not the 'depth' or what's referred to as the 'wet-look' that black and other dark colors exhibit (These black or other dark colors
do absorb some or all of the color spectrum)
IMO...One can obtain an even better gloss to a corrected CC top-coat paint-film by applying an LSP that will
'cure clear'...still allowing the BC's white color, or any other color for that matter, to still shine-through the CC paint-film and "the new top-coat-film...the LSP.
(Also IMO...Any good polymer/acrylic sealant; waxes/hybrids that include, but not limited to: P21S/S100, Souveran Sig. Series II, 3M Show Car, Meg's #26, Colly 845...comes to mind for accomplishing the above task.)
Hope this makes sense and, in some small way, helps some.
Bob