How would you approach managing a patient with ESKD on peritoneal dialysis who has a milky appearance of peritoneal effluent but low peritoneal fluid triglyceride levels?  

The key word here is "low" triglyceride (TG) levels. Peritoneal dialysis fluid should ordinarily be devoid of TGs with virtually undetectable levels, < 10 mg/dL. In a case I reported many years ago (Rocklin et al., PMID 10978409), SVC syndrome presented as cloudy dialysate with a TG level just 25...

Never seen it, but may be Chyle? Spin down, smear, and stain as a blood smear, looking for Lymphs? Do peritoneal lavage, short dwell while fasting, check again for lymphs, then after a heavy fat meal. Used this in a non-CKD patient with chyluria. If you find an answer, report it.