I've walked it with luggage a few times. Far from ideal but easy enough really. Exit T2 arrivals, cross the road to T2 Departures and turn right, keeping Departures on your left. Walk round to other side of building and you will see T3 ahead and LM over to the right. You can go in to T3 Departures and cross the bridge to LM. Taxi touts are a pain until clear of T2 concourse, then police are a pain to be allowed into T3 to use the bridge

Far easier is to get LM to meet you, contact them at [email protected] with your flight details. Rep will meet you with a named board, prior to immigration, and fast track you through all formalities and into the shuttle round to hotel reception