React class components - conditional styling based on props

I hope i got you right. There are two things you should put attention to:

First, correctBackgroundColor does not recognize props because this is out of scope, therefore, I would recomment to change it into a function, pass the props to it, and make the function return a style object.

Second thing, I would use style when applying the object to Paper, so the style of that paper would be a call to correctBackgroundColor with the props, like this:

<Paper id={this.props.id} style={correctBackgroundColor(this.props)} />

Final code:

import React from "react";
import withStyles from "@material-ui/core/styles/withStyles";
import Typography from "@material-ui/core/Typography/Typography";
import Paper from "@material-ui/core/Paper/Paper";

const styles = theme => ({
  typography_root: {
    fontSize: 12,
    margin: 10
  }
});
const correctBackgroundColor = props => {
  let bgSwitch = "none";
  if (props.ledIsOn === true && props.ledColorType === "Green")
    bgSwitch = "#00FF00";
  if (props.ledIsOn === true && props.ledColorType === "Orange")
    bgSwitch = "#FFA500";
  if (props.ledIsOn === true && props.ledColorType === "Red")
    bgSwitch = "#FF0000";
  if (props.ledIsOn === true && props.ledColorType === "Grey")
    bgSwitch = "lightGrey";
  return {
    width: 30,
    height: 30,
    border: "1px solid lightgrey",
    backgroundColor: bgSwitch
  };
};

class ColorChange extends React.Component {
  render() {
    const { classes } = this.props;
    let textToRender = (
      <Paper id={this.props.id} style={correctBackgroundColor(this.props)} />
    );
    return (
      <div>
        <Typography variant="p" className={classes.typography_root}>
          {this.props.textLabel}
        </Typography>
        {textToRender}
      </div>
    );
  }
}

export default withStyles(styles)(ColorChange); //with styles injects classes props with styles contained.

Code Sandbox