You can't do this with a single "normal" lens. Because the beam width needs to be 4.25 inches you need a lens wider than that (which is huge compared to normal optical components). The focal length of the lens would need to be 4.25 in/(2*sin(60 degrees)) ~ 2.5 inches = 63.5 mm which is smaller than the width of the lens, and you can't really make normal plano-convex lenses like this.

You have two options -- you can use multiple lenses (one lens to collimate, then a pair of lenses to step it up to a larger beam width), or you could also get ok results from using a Frensel lens -- one that is fairly close to what you need is here. The second option will probably be much cheaper, but may suffer from more aberrations.

You can't do this with a single "normal" lens. Because the beam width needs to be 4.25 inches you need a lens wider than that (which is huge compared to normal optical components). The focal length of the lens would need to be 4.25 in/(2*sin(60 degrees)) ~ 2.5 inches = 63.5 mm which is smaller than the width of the lens, and you can't really make normal plano-convex lenses like this.

You have two options -- you can use multiple lenses (one lens to collimate, then a pair of lenses to step it up to a larger beam width), or you could also get ok results from using a Fresnel lens -- one that is fairly close to what you need is here. The second option will probably be much cheaper, but may suffer from more aberrations.