Lith. pėda (foot, footprint), padas (sole) are the words that derive directly from PIE, *ped- pōds, not through Latin. And the words are very close
I disagree with you, but this doesn't mean that I am writing this to prove you wrong. I don't think your Lithuanian expression 'pėda' comes DIRECTLY from PIE language, and I will tell you why. I don't even think that PIE language, ever existed on the first place at all. That language, is an invention, created by the modern linguists, in an effort to give an answer to the similarity of the words, in different languages.I will keep it simple and clean. Our example:
pėda(lithuan)------piede(ital)------pied(french)---pie or pata(spanish)
they all come DIRECTLY from Latin NOT directly from PIE language
You should keep in mind, that Latin language is the language of the Latin Church, NOT the language of the Latin people(it became afterwards). I don't even need to look at the religion the Lithuanian people beleive, and just by that expression I could tell that at some point in time the Latin Church, must have been established in Lithuania.
Therefore, it is the the Latin 'ped' the real word which was pronounced pėda in lithuan, piede in italian, pied in french), pie or pata(spanish), languages which become as such after being a local respective dialect.
Now let's study the word itself, it variate from pé(portugese) to ped(+ending vowel) to the rest of the Romance languages, and it has the tendency to change the ending "d" to the easily pronounceable homologues, the voiceless "t". Now pat-a(spanish) is easily comparable to the Albanian put(ër-a modern ending), and this last one is easily comparable to the English foot(after phonetic transformation p--ph--f).
The English itself, although developed a new term from the original Latin "ped", maintained these root, to create relative terminology, like: pedestrian, centipede, expedite, impediment, pedometer, pedestal etc.
As for the Greek being an older version of the same Church language, preserve the same phonetic vector, from the Latin pes-ped to the Greek πους-πόδι, which "gave birth" to the other Greek word παις(AG)--παιδί(MG)=child.
This is the real way the language lexicon is acquired, within the language and from language to language. Then the PIE language is a scientific bs.