Am I obligated to continue paying a specific sum of money for every lie I commit, or was that only obligatory for the first lie after my oath?

If you swear, saying: "By God, when I lie, I will give one hundred riyals in charity," then you must give one hundred riyals in charity if you lie. This does not repeat with repeated lying, because the word "when" (عندما) does not imply repetition linguistically unless intended, unlike "whenever" (كلما). If you intended repetition, then the charity becomes obligatory every time you lie, because intention makes the wording equivalent to an explicit statement. Similarly, expiation is repeated if the repetition of breaking the oath was intended.