One litre per minute is 0.2641720524 US gallons per minute. The time unit is the same on both sides, so the conversion reduces to the volume conversion — which makes this the simplest pair in the flow category.
About the units
Gallons per minute, universally abbreviated GPM, is the standard flow unit for pumps, irrigation and plumbing in the United States. Litres per minute is its metric counterpart. Because both count per minute, the factor is exactly the gallon-to-litre factor and nothing more. The trap is the gallon itself: American GPM uses the US gallon of 3.785411784 litres, while British sources may mean the imperial gallon of 4.54609 litres, and the two differ by twenty per cent for the same nominal flow.
The exact factor
The exact value is 1 US gal/min = 3.785411784 l/min. Inverted, 1 l/min = 0.264172052358148 gal/min. Reference points: a domestic shower runs at 6 to 12 l/min, which is 1.6 to 3.2 GPM; a garden hose at 15 l/min or 4 GPM; and a domestic well pump might deliver 40 l/min or 10.6 GPM. Fire hoses operate at hundreds of GPM, where the conversion becomes a matter of equipment compatibility rather than convenience.
Where you meet this conversion
Pump selection and irrigation design, where American equipment is rated in GPM and European in litres per minute or cubic metres per hour. Pump curves, nozzle tables and filter capacities all carry one unit or the other. Plumbing fixture flow rates are regulated in both — American showerheads are limited federally to 2.5 GPM, which is 9.5 l/min, and to 1.8 or 2.0 GPM in California and a dozen other states, while European regulations set comparable limits in litres. Swimming pool turnover, hydraulic systems and coolant circuits use the pair throughout.