Li2O + 2KCl =2 LiCl +K2O: Is it a feasible Reaction?
Although every reaction is reversible in nature, let's try to understand where the equilibrium might be biased, i.e. whether the reactant side favoured or the product side.

A rule of thumb while predicting feasibility is to remember, a reaction where you can get a weak acid from a strong acid is feasible.

$$\ce{Strong Acid -&gt; Weak acid}$$

In your case we're dealing with $\ce{KCl}$ and $\ce{LiCl}$. The acidic or basic nature or salts is determined by the extent of hydrolysis of its ions. Ions from a weaker species undergo hydrolysis while ions from a stronger species don't. Another way to look at this is to compare the acidic and basic strengths of the acids and bases which formed them in the first place.
$$\ce{LiOH + HCl -&gt; LiCl + H2O}$$
$$\ce{KOH + HCl -&gt; KCl + H2O}$$
Notice that $\ce{HCl}$ is common to both of these species, so we have to just compare the basic strengths of $\ce{LiOH}$ and $\ce{KOH}$. Down the group (in alkali metal hydroxides) basic strength increases. So $\ce{KOH}$ is a better base. And thus $\ce{KCl}$ is a weaker acid. Since we're making a stronger acid from a weaker acid, the reaction can be termed as unfeasible.