For the Same Reasons Humans Do
Lizardfolk, cold blooded or not (that tends to flip between settings) would still want clothing for thermal insulation. I'm going to go for a cold-blooded approach, but this is true for lizardfolk in general. In cold weather furs et al would be a requirement to keep warm, which would be very important in a cold-blooded species where warmth=agility/alertness to a certain extent. It wouldn't be as efficient as it is for us humans, because we radiate heat as a matter of course, but it'd still be better than wandering around naked! I'd imagine winter/arctic lizardmen spending their mornings around the fire largely naked to absorb as much heat as possible, then adding insulation and going about their day.
In a hot environment they would wear flowing garments like Bedouins do to help keep cool, as they have no ability to sweat like humans. Of course if they evolved from desert-dwelling reptiles they may not need quite as much covering as the Bedouins do. If they were out and about at night however I could see them wearing something similar to our arctic lizards, since deserts gets surprisingly chilly.
Anything temperate/seasonal would have the traditional movement from more to less clothes and back again seen everywhere. Though there may be a stylistic choice to wear things that are easily removeable. I'm imagining something like a dress, wherein the top could peel off. Or a jumpsuit that can be unzipped around the waist. 671
That would let your lizardfolk warm up at will without forcing them to either discard or hand-carry whatever clothes they wore when it was colder.
Then of course you can't discount cultural/religious/biological reasons for doing it. Maybe they all wear hats because they have crests that raise/change color when they get aroused/angry/sick/hungry/whatever, and it becomes poor manners to display that to others in public. Maybe a long tail the epitome of sexy, so they wear tail coverings to make their tails look thicker/longer. The tail coverings become more and more elaborate, and the belt that used to hold them on turns into suspenders/shirts/clothing in general as a status symbol. Or maybe it sticks to just tails. Maybe the mid-scales are considered religiously unclean, and thus should be hidden from view. The social possibilities are endless!
That's what I got for main body coverings. Gloves and shoes would probably be a bit less common, as lizard claws/feet are more durable than human ones. But boots in cold/wet weather or over hazardous ground and gloves for very hot/cold object handling would be common enough. 802