In a mechanical oscillator there can be different forces (air resistance, friction, etc.) that keep the system from being ideal as we discussed with drag. Are there other factors besides resistance that would stop an LC circuit from being ideal? (How do they lose energy?)

In a real circuit, generally ohmic energy loss, i.e., from an $iR$ voltage drop (for which mechanical analog is a force proportional to velocity, like drag), is actually a pretty good model, and is associated with energy loss via heat (usually the dominant form), light, sound, etc.. In a real circuit, the capacitor and inductor might not be ideal-- there can be stray capacitances and inductances, effectively in parallel as well as in series, which can change the circuit behavior... or there can current leakages in or out of the system, environmental electromagnetic noise, vibrations changing the properties of the system, and all kinds of other time-dependent environmental effects... the real world is a messy place!