What is your approach to monitoring a patient with SLE who has persistent hypocomplementemia on hydroxychloroquine, but clinically has resolution of cutaneous symptoms and no other internal organ manifestations of disease?

Per the subtitle under your question, an undetectable C4 with low C3 makes me wonder about the possibility of a homozygous C4 deficiency, of whom 75-80% of patients have SLE with a high occurrence of lupus nephritis (Yang et al., PMID 15294999). You can consider genetic testing (primarily for genetic counseling of the patient's children) (Margery-Muir et al., PMID 24757030), but otherwise, it would not change my management. I have not seen anything in the literature on this, but it would be interesting to order an EC4d level (Ramsey-Goldman et al., PMID 29214038). If it were negative, that should confirm a homogenous deficiency (maybe there is a case report, but I cannot find any).

Although SLE patients with stable abnormal serologies appear to have a good prognosis (no damage accrual) when clinically quiet (Steiman et al., PMID 22162433), a review by Kostoulou et al., PMID 35067068 recommends vigilant monitoring in this patient population due to a potential for increased risk for flare. This patient is at a particularly higher risk for flare. Patients with homozygous C4 deficiency tend to have more severe disease, so the stable hypocomplementemic literature would not necessarily apply to this case.

Otherwise, I would treat this patient the same as all my SLE patients with hypocomplementemia. With C3 being low, it suggests ongoing complement consumption and hence some active immune system activity. I'd label the patient in my records as "serologically positive but clinically quiescent." 

Watch the trend of the patient's C3 over time. If there is decreasing C3, that could be predictive of a possible subsequent flare (I'd readdress everything in the last paragraph). 

I am diligent about screening for lupus nephritis in all my asymptomatic SLE hypocomplementemic patients q 3 mo with a urinalysis with random urine/protein creatinine ratio, chemistry panel, anti-dsDNA, anti-C1q, and CBC (for cytopenias, not lupus nephritis). I would do the same in this patient, especially since homozygous C4 deficient patients are at higher risk for lupus nephritis. 

I would not treat the abnormal serologies as there is no evidence that we achieve any benefit from doing so. I would ensure the patient is on hydroxychloroquine and monitor HCQ whole blood drug levels aiming for a level of 1000 ng/mL (Petri et al., PMID 33403833, and Costedoat-Chalumeau et al., PMID 17009263) to 1200 ng/mL (Petri et al., PMID 31532077) while also using levels to assess adherence. Each visit I'd remind the patient about nonpharmacologic avoidance of triggers such as strict UV protection (eg wearing sunscreen daily, wide-brimmed hat outdoors, using only LED bulbs in the home and workplace, etc), eating an anti-inflammatory diet (rich in omega-3 fatty acids and resistant starches +/- probiotic-rich foods), not smoking, working on good dental health (Sojod et al, PMID 34063235), getting at least 7 or more hours of sleep (Young et al., PMID 29804502), decreasing stress (Patterson et al., PMID 36537191) and daily mindfulness, and maintaining normal body weight (Patterson et al., PMID 29740985) while also exercising to reduce CV events.

I agree with Dr. @Dr. First Last's nice explanation. I would just add a few things.

Due to copy number variation we see many patients with low C4 without any contribution to their disease activity. Unless we had prior normal values, it's hard to distinguish these individuals. Also complement deficiency (C4 or other classical pathway early components like C1Q, C2) can increase the risk of lupus, lupus nephritis, with or without concomitant infections. Patients with complement deficiency typically present early, refractory disease with infections, and would have a high prevalence of nephritis. Significant complement components are synthesized in the liver, and others at extrahepatic sites. Chronic liver disease and cirrhosis may sometimes confuse the interpretation of the C3, C4 level interpretation.

Besides clinical reasoning and assessment, we could use some additional tools. They could be Total complement (CH50), complement split products (EC4d, LC4d, etc), and complement genetic testing. CH50 is relatively cheaper and would give you information about the classical pathway functioning. I would pursue the rest if it is going to help me change the management of individual patients (as they are relatively expensive).