Alex Lifeson playing one of my favorite guitars, the Gibson ES-355 semi-hollow body in white finish. Sweet!!
Alex Lifeson was pretty much an under-appreciated guitarist. Since Rush was a three piece band, his guitar was utilized for a lot of rhythm playing. His guitar work was sometimes left in the background while the drums and bass were the main focus on some songs. Alex took a section of "Spirit of the Radio", where most guitarists would consider rhythm chords, he chose a complicated string of 32nd notes and hammer-pull offs! He is very disciplined and plays what's best for the song. His phrasing of his solos is perfect. He doesn't miss a beat or a fret. His use of natural and artificial harmonics create his own brand of guitar virtuosity.
His classical playing is in a league all its own. Listen to "Broon's Bane" off the live album Exit...Stage Left
As far as equipment goes, at the concerts I attended early on, Alex Lifeson used Gibson guitars (ES-335, ES-355, and Les Pauls), HiWatt and Marshall amps. He used a ton of effects mostly chorus, echo and distortion.
I went to two or three Rush concerts back in the late 1970's. All were at the Stanley Theatre in Pittsburgh PA. Styx opened for them at one concert, not sure who opened the other times. It was a really thrilling time back then. Rock was in the forefront of music (long before disco) and it seemed like it would go on forever. I haven't been back for a show even though they're still together after all these years. Hopefully, maybe this year will be the reunion between my inner teenager and my current self.
Rush soon were pushed down in my rock and roll thoughts by newer and different guitarist. Eddie Van Halen, Neil Schon, Tom Scholz to name a few. I still bought new Rush albums but wasn't very interested in their new phases in music. Don't get me wrong, I just like the earlier Alex Lifeson licks better.

Alex Lifeson, Geddy Lee and Neil Peart, coming on stage and the wail of 2112 through Marshall amps, is something that still resonates within my mind and memory! Oh and by the way, my email since I've been on a computer for over fourteen years is still, and will always be, robrush54@gmail.com!
(One more thing, I did end up buying The New York Dolls record a few years later, not even close!)
Here's a great video of Alex showing us his current stage set-up!