Some people are concerned about suspected health effects from parabens, among other ingredients, and glycerin can exacerbate yeast infections for some people, but I don't think it's a clear-cut conclusion that Liquid Silk is inappropriate for vaginal use. I think it's safe for you to continue using it if you've never had a reaction to it before, and it depends on your level of comfort with the ingredients and whether you believe they may have any unknown health effects.
Liquid Silk has a complex formulation with more ingredients than some other lubes, however I suspect that's how it can achieve such a hybrid performance, with the features of water-based and silicone lubes and the silky feeling of lotion. It contains silicone (dimethicone), some oily compounds common to lotions (isopropyl palmitate, sorbitan stearate, cetearyl alcohol, glyceryl stearate), and typical water-based lube thickeners (propylene glycol, cellulose polymer, polysorbate 60, and parabens). Some of the ingredients in Liquid Silk are known to be toxic in high doses (like phenoxyethanol, used as a preservative here) and some other lubes do have a shorter ingredient list, although their performance will also be different.
The ingredients in Liquid Silk are generally accepted as safe in the quantities present. If you're concerned you may want to experiment with alternatives, which will feel and perform differently.