The part which struck me as being somewhat marxist is the part when Lear, the fool, Kent and Edgar go to the hovel after they are banished from his castle. Here is where Lear must endure this storm that has come. 
Here his character begins to see what is actually going on. Here he sees how the rest of the kingdom
lives.  

Poor naked wretches, whereso'er you are,
That bide the pelting of this pitiless storm,
How shall your houseless heads and unfed sides, 35
Your loop'd and window'd raggedness, defend you
From seasons such as these? O, I have ta'en
Too little care of this

Here he is feeling what his people feel when storms like this come and how he has done nothing to help them. He also sees how his daughters have mistreated him.

But I will punish home: 20
No, I will weep no more. In such a night
To shut me out! Pour on; I will endure.
In such a night as this! O Regan, Goneril!
Your old kind father, whose frank heart gave all,--
O, that way madness lies; let me shun that; 25
No more of that.

I would interpret this as Lear being the upper class in terms of wealth over the people of his kingdom, but at the same time he is lower class compared to his daughters.