What are the effects of Lithium Dioxide on the body?
Is it safe to inject Lithium Dioxide into our body?


No. It will do bad things.


  Does it have any side effects?


Yes. It will do bad things.

As lithium is an alkali metal, it does not usually form covalent bonds, so we should treat whatever it makes as ionic. The common form of lithium oxide is $\ce{Li2O}$, which is not that scary. "Lithium dioxide" would be $\ce{LiO2}$. This implies that that lithium is tetravalent, as $\ce{Li^4+}$. This is not possible, as it requires lithium to give away 4 electrons but it does not have 4, only 3. This means that oxygens are in the superoxide form: is $\ce{O2-}$ instead of the more stable $\ce{O^2-}$. That is definitely not stable in isolation at ambient conditions (unlike other alkali superoxides) and I'm not sure where you will get that stuff.

The result of that is that one molecule (or whatever it is) of $\ce{LiO2}$ will really want to convert itself to $\ce{Li2O}$. The superoxide ion is not going to do fun things. For each $\ce{O2-}$ you're going to need 3 more electrons to make it stable, so that is very strong oxidiser.

As a comparison to what this could do to you, I would guess it would be worse than injecting pure hydrogen peroxide (you have about 5% of that in hair bleach), or pure sodium hypochloride (similar 5% in kitchen bleach). This is definitely not going to treat "palladium poisoning" because it will probably kill you beforehand.

That said, using an oxidiser (such as lithium dioxide) to treat noble metal poisoning (such as palladium) seems dubious to me. I'm not a doctor, but I reckon that there are better method to treat that. So why lithium and palladium? I guess is sounds more credible than "using titanium to treat potassium poisoning" but less credible than "using dysprosium to treat beryllium poisoning", both of which make absolutely no sense as "using lithium to treat palladium poisoning".