Well, while there isn't anything in the way of official lore for those items or the people that once owned them, you can figure a few things out just by looking at them. I'm gonna use Randuin's Omen and Sterak's Gage as my examples here, since they're the easiest.
Randuin's Omen a distinctly Demacian object (bearing the whole sword+wings crest and everything), and, on top of it seeming to be a petricite tower shield, it seems to be a particularly celebrated item, since the top edge of the shield is decorated with blue streamers/ribbons.
From this, we can assume that Randuin (who Illaoi refers to as a "she" - though it isn't really known whether or not Illaoi's heard of her or if she's just guessing - I'll get to her quote in a bit) is a decorated war hero of Demacia, whose tower shield must have been pivotal in repelling some invading army. She could have been a member of the Dauntless Vanguard during a time before Garen was a part of it - or they could potentially be soldiers of the same army in the same age.
Whatever the case, Randuin's Omen also hints to it being a symbol of victory (as many massive objects made of petricite seem to be, Galio...), hence it being named "Randuin's Omen."
Omen
noun
an event regarded as a portent of good or evil.
Which, while that says more about Demacia as a whole than it does about Randuin, it can be assumed that her shield was considered to be as much of a good-luck charm/symbol of victory as Durand's greatest work.
And, as a little bit of extra stuff, Illaoi's quote upon purchasing Randuin's Omen sheds a little extra light on the people of Buhru - or maybe just herself.
"Who is Randuin? Was she a priestess?"
The quote of course refers to the possibility that Randuin - in Illaoi's eyes - could have been the equivalent of a priestess for her people. A well-built warrior sending messages of her god through a massive, weighty implement. Randuin's Omen, to Illaoi, is another peoples' Eye of God.
Sterak's Gage, on the other hand, looks noticeably of Noxian make. A hefty iron gauntlet, made of dark metal and thrumming with a violent energy. It looks like it belonged to somewhat of a legendary or powerful soldier, and could very well have belonged to a Noxian warlord or general. Obviously, though, whatever position Sterak held, he held it on the frontlines.
Sterak's legacy seems to have bled into his gauntlet as well, seeing as how those who wear it can be brought low in a fight, only to redouble with greater strength than before. Surely, Sterak must have had the color beaten out of him countless times, only to remain unbowed and fight back even harder.
But, what I find interesting is, like with Randuin's Omen, Sterak's Gage has an interesting name choice.
Gage
noun
a valued object deposited as a guarantee of good faith.
verb
offer (a thing or one's life) as a guarantee of good faith.
Sterak's Gage could be his symbol of good faith, or it could be emblematic of a willingness to offer his life as a show of faith. This could, naturally, work well into his being a warlord or general - he would want his soldiers to have faith in him as a leader, so, what better way to do that than to promise he'll get them through, or he'll die trying?
These are just two examples of stories ever-so-subtly hidden in as little as an item icon, and, while, again, none of these theories are remotely canon, they are interesting to think of and see how they work in the world of Runeterra.
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