I've found for lime scale on glass viakal, etc, is all but useless unless it's very recently deposited lime scale.
I use diluted patio cleaner as it's an acid. I dilute it 1:4 as over the years, I've found that works best.
Wet the brick work underneath the window first and also wet ground/floor/patio/etc. Spray on with a hand spray bottle fairly generously to give a light even wetting on the affected area on the glass and use a sponge with a green abrasive bit on it. It takes seconds to remove the lime scale and then rinse off with plenty of water not because patio cleaner will affect the glass in any way, but because of streaks from the run off over the brick work, etc.
Patio cleaner will discolour aluminum, metal, stainless steel (door handles) etc, so be carefull and wear latex gloves and make sure you don't breathe the spray by mistake.
I used to do one house 2 monthly that was a well priced job and they had a dripping over flow that drippped over a ground floor window. Using patio cleaner it took seconds to remove the lime scale.