Yeast can act on glucose in solution perhaps even more easily than it can use sucrose. Glucose is the archetypal "brewer's sugar" that is directly available for fermentation, so there would be no inhibition of fermentation on that point.
Caffeine does not inhibit yeast fermentation to any degree in reasonable concentrations (eg like a cup of coffee) as, for example, strong coffee infusion is often added to speciality brews as a flavouring agent.
What will affect fermentation of Lucozade the presence of "preservatives" like potassium sorbate (or any other "preservative" present). Sorbates inhibit the growth and action of saccharomyces so fermenting Lucozade would be rendered more difficult if not impossible by the presence of that preservative.
A high concentration of sugar in solution can also inhibit yeast - eg syrups, treacle and molasses resist fermentation. I am not sure if Lucozade is a sufficiently concentrated glucose solution to do that on its own or whether it is still sufficiently dilute to ferment and thus sorbate is added to prevent that.
But one might well ask - why ferment Lucozade? If one was particularity driven to do so, then it would be cheaper and more efficient to make up a flavoured glucose solution, add some caffeine and proceed from there. Although one might still ask, "why?"...