Class is something that is incredibly evident in both of these works, both in the way that it separates and delineates society. In Chapter 4 of Lucky Jim for example, Dixon sees Christine Callaghan for the first time and finds that class anxiety descends on him as he looks at a woman who is beautiful and irresistibly tempting, but ultimately out of his reach because she is from a different class:
The sight of her seemed an irresistible attack on his own habits, standards, and ambitions: something designed to put him in his place for good.
She is unavailable not only because she is dating Bernard, but also because she is completely different from any other woman that Dixon would normally date, and this is why she is described as an "irresistible attack on his own habits, standards, and ambitions" and is seen by him as "putting him in his place for good." This helps explore the theme of Dixon's hope of entering a new and different social class from the one he currently occupies, and the massive difficulties that he faces as a result.
In Howards End, it is Leonard Bast who most clearly wishes that he could be part of a different class. Note how this is signalled when he has tea with the Schlegels after the Beethoven concert and is amazed at their level of knowledge and the erudite conversation that they have:
If only he could talk like this, he would have caught the world. Oh to acquire culture! Oh, to pronounce foreign names correctly! Oh, to be well informed, discoursing at ease on every subject that a lady started! But it would take one years. With an hour at lunch and a few shattered hours in the evening, how was it possible to catch up with leisured women, who had been reading steadily from childhood?
Unfortunately, just like Dixon, he finds that what he contemplates is impossible. For him, who has to work for a living, and only has very little spare time, he has no chance of being able to gain the level of learning that would enable him to converse with them as an equal. He is left, like Dixon, to contemplate a world that it appears he can never be a part of because of his class.
A good thesis statement to use to explore this theme would therefore be:
In Lucky Jim and Howards End class is presented as a barrier to social mobility.
This thesis statement would enable you to explore the theme of class and how the social conditions of the characters prevent them moving up in the world.