Reference to theme's primary color instead of a specific color in Material UI

Yes you have! using muiThemeable..

import muiThemeable from 'material-ui/styles/muiThemeable';
class LockIcon extends React.Component {
    render() {
        return(
            <ActionLock color={this.props.muiTheme.palette.primary1Color} />
        )
    }
}
        export default muiThemeable()(LockIcon)

from material-ui docs

Adding how to access theme colors in material-ui v1.0.0 (currently beta) Using withTheme component.
Also check the following Example.

import React, {Component} from 'react';
import { withTheme } from 'material-ui/styles';

class WithThemeExample extends Component {
    render() {
        const { theme } = props;
        const {primary, secondary} = theme.palette.text;

        return (
            <div>
                <div style={{color: primary}}>Hi in Primary color</div>
                <div style={{color: secondary}}>Bye in Secondary color</div>
            </div>
        );
    }
}

export default withTheme()(WithThemeExample);

If you're using React v16.8.0 and Material-UI v3.5.0 or greater, you can utilize the useTheme() hook:

import { useTheme } from '@material-ui/core/styles';

function LockIcon = () => {
  const theme = useTheme();

  return (
    <ActionLock color={theme.palette.primary1Color} />
}