NewHilux.net

Can you install a 3 inch strut without changing the stock control arms and could you fit 32 on without issues?

Sure, you can do all that WITH issues. Alignment is one thing and depending on the tyre brand/wheel offset you may need to cut/remove the mudflap.

Have a search around the site. There are threads on fitting 32in tyres in both the n70 and n80 sections - much the same info really. Plenty of builds talking about suspension lifts.

FWIW 2in is legal and widely regarded as the sweet spot for lifts on the hilux.

3" you will need a diff relocating set up not a cheapo drop.
You will fowl the strut on full droop on the standard UCA,

2" is the safe bet with 32" tyres and minimal mods And as above an alignment is differently needed.