Any difference between “I have a lot of work to do” and “I have a lot of work to be done”?

Solution 1:

The difference is that the first sentence clearly states that the speaker has a lot of work which they specifically must do, while the second sentence is not really valid English as it mistakenly conjugates the doing in the passive voice, as if it applies to the work rather than to the agent (I, in this example).

By de-emphasising 'the work', this should be made more clear.

I have (a lot of work) to do

From this we should see that

I have (a lot of work) to be done

makes far less semantic sense, and could possibly imply that there is a lot of work which needs to be done on me, which is highly unlikely to be the intended usage, unless it were to be uttered during a conversation about impending plastic surgery.

There is a lot of work to be done would be far more common usage, and makes it equally ambiguous about who is expected to do the work.

Solution 2:

"I have a lot of work to do" would communicate that the speaker is the person who will be doing the work while the second sentence is incorrect as it should communicate that "the work to be done" is more important than the person doing it. In other words, the "I have" in the second sentence "I have a lot of work to be done" should be replaced by "there is".

The correct sentence then in the passive voice should be,

There is a lot of work to be done.

This sentence is used when the object work takes predominance over the subject "I" and the "I" is understood. The first sentence you used communicates that you are responsible for the work to do and the second, in the corrected form is more ambiguous because it could mean that someone else could do the work and not necessarily you.