Final answer:
The most likely etiological agent causing the UTI in this case is Escherichia coli (E. coli), as indicated by the presence of a lactose-fermenting gram-negative rod in the urine culture and associated symptoms and lab findings.
Step-by-step explanation:
The most likely etiological agent in this case is Escherichia coli (E. coli). This diagnosis is based on the laboratory results showing a lactose-fermenting gram-negative rod, which is a characteristic of E. coli, and the presence of white blood cells in the urine sediment suggestive of a urinary tract infection. E. coli is the most common cause of urinary tract infections (UTIs), and the presence of nitrites on a urine dipstick test can further indicate its presence, as this organism converts nitrates to nitrites.
The symptoms presented by the patient, such as urinary frequency, urgency, dysuria, and hematuria, along with an elevated white blood cell count and significant growth of bacteria in cultures, support the diagnosis of a UTI caused by E. coli.