Lithium has a very clear interaction with some NSAIDs, but not all of them.

Lithium blood levels rise with concurrent use of ibuprofen, sometimes to toxic levels (close to doubling, in some subjects).

However, there is no interaction with tylenol (acetominophen, paracetamol in the British system).

Here's a quick quotation from a private website:
"A marked and rapid rise in serum lithium levels (+60%) with intoxication may develop in patients given clometacin or indometacin (indomethacin). A more moderate rise (+15–34%) occurs with diclofenac and ibuprofen, but much larger rises have been seen in a few patients. Increased serum lithium levels and/or intoxication have also been seen in small and variable numbers of patients when given flurbiprofen, ketoprofen, ketorolac, lornoxicam, mefenamic acid, meloxicam, naproxen, niflumic acid, phenylbutazone, piroxicam or tiaprofenic acid. Sulindac is reported to increase, reduce or have no effect on serum lithium levels. Aspirin, lysine acetylsalicylate, sodium salicylate and paracetamol (acetaminophen) appear not to interact. "

Aspirin and tylenol are good choices, so you could use that Oxycodone APAP 10/325mg you mentioned, without pharmacological interaction. You may notice a symptomatic interaction (the two may not promote a feeling of wellness, when taken together), but it is not due to any reported drug interaction. There is no reported interaction between lithium carbonate and any member of the opioid analgesics.

About the Lasix....here's another quote from the paysite: "The concurrent use of lithium carbonate and furosemide (frusemide) can be safe and uneventful, but serious lithium intoxication has been described in a few individuals." In the detailed evidence shown, most people have no interaction of any sort between these two drugs, but for some people, the Lasix can bring on toxic lithium levels. It is the responsibility of the doctor prescribing the diuretics, IMHO, to ensure that you're on one that is safe for you.

I couldn't find anything on the lisinopril interaction.

Lar