I suggest you get a few of these:-
https://uk.rs-online.com/web/c/batteries/non-rechargeable-batteries/d-batteries/?searchTerm=lithium thionyl chloride
Lithium Thionyl Chloride batteries in D-cell size are nominally around 18 Ah and 3.6 V, so one will run 4 mA for 7 months, with enough voltage to light an LED.
They are a bit over twice the voltage of an alkaline cell of the same size, so only 1 is needed to power an LED. The voltage of the Lithium Thionyl Chloride batteries stays nearly constant as the battery is discharged, which means that you don't have to worry about a varying voltage. If it works when new, and the current is low enough, it will work for 7 months. The voltage of an alkaline cell reduces as it discharges.
If you want a longer time or more current, put more in parallel.
You will need a resistor to limit the current. There are various calculators for the resistor value, and one is at
https://mtrak.co.uk/led_calculator.html but you will need to know the LED voltage at the current you want, so you might end up adjusting the resistor up or down a bit for your particular LED, to get the current to the value that will allow the 7 months of use.
Lithium Thionyl Chloride batteries are really expensive, but as you are only making one or two of these, you could spend a lot of time designing and testing a circuit with cheaper batteries. Also the Lithium Thionyl Chloride batteries have a very good energy density and they are perfectly suited to low power loads. Alkaline batteries will be a lot bigger for the same energy, but would be better for high power loads like motors.