I just completed this mission a few minutes ago, so I know just what you are going through. I tried many strategies: one was to try to take out all of the gang members. After multiple tries, I realized this wasn't the thing to do because not only is Diaz's gang overwhelmingly deep in numbers, but they also carry deadly assault rifles that will destroy a car in perfect condition in a matter of seconds. On top of that, you won't have enough time to kill off the gang members and save Lance.
Then I tried different strategies based on the cars I would use to get to the junkyard. I tried picking a durable car and getting through the junkyard, but this didn't work because, like I said before, no car stands a chance against those assault rifles. This prompted me to try a fast car in hopes of being able to speed through the junkyard before they could shoot up my car. This is the strategy that worked for me.
Before you start the mission, get some Uzi ammo if you don't already have plenty. Then get full health and full body armor. Next, get a relatively fast car. Once you get to the junkyard, plow through the Sentinel being used to block the way at the rear. I found that this allowed me to continue through the junkyard w/o having to recover too much. Speed on through the junkyard, making sure not to run up on the sides and get the car caught on obstacles. Gang-men will be at the front and side. You can choose to run these people over or shoot them drive-by style. But when I completed this mission, I did neither. Instead, I continued on and ran over the people in front of the shed where Lance is.
About this time, my car blew up. I then killed the guy inside the shed with my Uzi, then ran to Lance. After the cutscene, I ran into Lance intentionally as if "activating" him because on previous tries he would not follow me when I was running. I proceeded to run outside the shed, ignoring the people shooting at me and getting into the second Sentinel parked to the left of the shed. Lance got in then I ran over the gang-men shooting at me while I drove towards the entrance of the junkyard.
Once I got there, I exited the Sentinel and got in the first one that was being used to block the entrance, since it wasn't as beat up. I knew Diaz's men would be after me, so I took an alternate route. Immediately after driving through the entrance, I turned right and crossed a bridge leading to some docks, then hung a left and made another right to turn back onto the road. I drove down this road, going away from the hospital, then made the necessary turns to get me on the main road leading to downtown. Diaz's men never saw me, and I never saw them. Drive on to the hospital to complete the mission.
