Setting React Navigation (React Native) drawerLockMode to `locked-closed` only when drawer is closed. (Don't allow open gesture, only close gesture).

gistfile1.txt

Add Redux action setDrawerOpen to set a boolean Redux variable (drawerOpen).

In your contentComponent update the Redux store when drawer open/close is detected:
componentDidUpdate(prevProps) {
        if (
            prevProps.navigation.state.isDrawerOpen !=
            this.props.navigation.state.isDrawerOpen
        ) {
            this.props.setDrawerOpen(this.props.navigation.state.isDrawerOpen);
        }
    }
}

Wrap the "Screen" component with this HoC which sets navigationOptions for drawerLockMode to a navigation param and updates when the Redux store updates:

import React, { Component } from "react";
import { connect } from "react-redux";

export default function withDrawer(Wrapped) {
    class Wrap extends Component {
        constructor(props) {
            super(props);
        }
        componentDidUpdate(prevProps, prevState) {
            if (prevProps.drawerOpen != this.props.drawerOpen) {
                this.props.navigation.setParams({
                    isOpen: this.props.drawerOpen
                });
            }
        }
        static navigationOptions = ({ navigation }) => {
            let drawerLocked = true;
            if (navigation.state.params && navigation.state.params.isOpen) {
                drawerLocked = false;
            }
            return {
                drawerLockMode: drawerLocked ? "locked-closed" : ""
            };
        };
        render() {
            return <Wrapped {...this.props} />;
        }
    }
    const mapStateToProps = state => {
        return { drawerOpen: state.drawerOpen };
    };

    const mapDispatchToProps = {};
    return connect(
        mapStateToProps,
        mapDispatchToProps
    )(Wrap);
}