As far as I know, the convention centre has no lockers. At C3, I had small day pack so I could carry the loot around plus snacks & drink. I expect the prices for snacks/drink to be high as usual.

The Wilshire Grand is approx 0.9 of a mile. The Holiday Inn where Jesse & I are staying is 0.2 of a mile so we run across the street & drop stuff off & run back.
The maps below should help you out planning any walking routes needed.
This PDF map shows downtown hotels & moreInteractive downtown L.A. MapI think there was an area in the centre at C3 where you could mail stuff out, not sure about this centre tho. The hotel Bob & I stayed at had a UPS store around the corner so we mailed most of our stuff back & Bob lost 1 item.

Yep, customs up here is a killer. Smaller items (loose figures) that can fit in a jacket pocket well no claim.

But yeah, mailing stuff out from the US would be better.