Theere is a useful drug interactions checker:-
https://www.drugs.com/drug_interactions.html
And one could always Google the SPCs from the EMEA for each drug.
The inteactions checker states that the lithium itself may alter the glucose level but doesn't note any particular interaction known.
Given the increased risk of heart attack and stroke in bipolar disorder, using a diabetic agent that decreases the risk of vascular disease like empagliflozin seems a sensible idea.
The question hinges on renal function; in trials like EMPA-REG, and CANVAS, empagliflozin and canagliflozin preserved renal function which is invaluable; however, during intercurrent illness eg gastro-enteritis tummy bugs, there was an increased risk of renal impairment. If one gets lithium levels into the toxic range, then this can lead to dehydration and renal impairment which would be worsened by the empagliflozin.
One cannot be too careful about interactions with lithium, so if worried, it is eay to check a lithium blood level, and during tummy bugs, drink plenty of fluid and if you cannot keep your food and drink down, get medical advice that day.
The main meds to avoid with lithium are non-steroidal anti-inflammatory drugs eg ibuprofen which for some reason is still available over the counter and diuretics.
Best wishes