Hey Daniel, just a note here that you may already be aware of, so bear with me.
Don't forget that the Portal Road is closed between Lone Pine campground and Hogback Road. This, as Doug has pointed out, you need to either take Movie Road to Hogback or Moffat Road to Hogback and then exit Hogback just below the first road switchback (where the lower gate is). These roads are dirt and sand, with washboard surface at times. So, you need to anticipate about 9 miles on a dirt road. I did take each road to see which one might be the best way to get to the Portal Road and found taking Moffat Road to Hogback the best way.
Now, I was up in Lone Pine last and was surprised to find that the lower gate was hard closed. The gate was locked. I had to, as did other hikers have to walk the 4 miles (or so) to the Portal where the trail starts. There were some angry hikers not anticipating the extra miles.
That was last week, however, I would call Inyo County Roads: 760-878-0212 - Public Works Roads, and find out the current status so that you can anticipate your starting point.
Paul