Why do lump sum transfers affect prices? Let's suppose that I want to maximize total welfare (Social Planner Problem) using lump sum transfers to individuals.

It's known then that the price ratio changes relative to when there are no lump sum transfers. Total income and total endowments are fixed in the model, only distribution of initial endowments is changed between the individuals by planner.

My Question is :

Why do lump sum transfers affect the price ratio in the social planners problem?
Prices (and hence price ratios) carry information about what people want, and what is supplied.

You're only changing initial endowments, hence you're not affecting what is supplied. However, as you change the initial distribution, you change what each individual wants, and possibly (not necessarily) also what the economy as an aggregate wants. This change in wants and haves is reflected in prices.