I was having dinner, but I couldn't finish it all up. So my mom said:
Eat it up, I haven't given you much/a lot.
Eat it up, it wasn't too much.
Something like soup:
Finish it, I haven't given you much/a lot of soup.
And about Indian dal (semi-solid)
Finish it, I haven't given you much/a lot of dal.
And about something solid, will it still be the same?
I don't know the best way to describe it.......
Yes it would be the same. "Finish it, I haven't given you much/ a lot of meat" is a perfectly acceptable sentence.
With regards to something solid, would it still be the same?
Yes, the same phrase would apply to liquid, semi-solid and solid food items. The state of matter of the food does not affect the phrase.
How would you put "much" or "a lot" in a sentence – "I haven't given you much/a lot" or "I haven't given you much/a lot of soup/vegetables"?
In casual speech, I would simply leave the phrase hanging, without specifying the actual noun. Consider:
While all the above are valid, I would most-likely phrase like the last option—with emphasis on that—as it subtly delineates between the speaker's opposition to the listener's opinion that they have been given too much, and not giving as much for a specific reason (e.g. due to the listener being on a strict diet, or the cost/availability of the food).
I do note that injecting and emphasising that is still applicable to the above sentences but, in that case, it is more likely a passive apology (becuase you are unable to give more) than the encouragement to eat more:
If you felt that you needed to specify exactly what food you had deliberately reduced, I would also use many for countable food items. This gives you options, such as:
...but you could substitute a lot, in most cases:
