"Da Bronze James" is a "name soundalike" to LeBron James.
"Name Soundalikes" is often a word/sentence that sounds similar to a famous person's name. "Da Bronze James" being one of the more popular ones". Other popular ones are "Water Weight" (Walter White), "Brain" (Brian From Family Guy) and "Better Console" (Better Call Saul).
The "Name Soundalike" is often an image of a line of text followed with a red circle around the word/sentence that is supposed to be the "Name Soundalike". The image of who the word/sentence sounds alike is often in the image too, with an arrow pointing away from it towards the circle.
A twitter account going by the name "Name Soundalikes" posts a ton of these images with a ton of users liking each one of them.
On YouTube, there are several videos of usually "friends" laughing together while looking through the images.
Person 1: How many soundalikes of LeBron James do you know?
Person 2: Uhh, Da Bronze James, The prawn bay... uhh...