A better way of saying this sentence would be: "There are many types of calligraphy artwork to display." "There is a lot of calligraphy artwork to display." "There are many calligraphy works of art to display."

It is not incorrect to say "There are a lot of calligraphy artworks to display.", but you could also say "There are many calligraphy artworks to display." The second one just sounds better.

There is a lot of calligraphy artwork on display. You should be using artwork in the singular. Further, I assume you are telling about the artwork already displayed somewhere. Happy learning !

thank you for your detailed answer~

I only saw Muhammad's post after I posted. And our posts seem to contradict each other. There are different uses of this word "artwork". So as an uncountable noun, we would say "artwork" For example, She submitted the "artwork" (all the pictures and photos) to be used in the magazine article. As a variable noun, we can use "artworks". For example, "The museum contained 2000 modern "artworks" .....which is a magnificent collection of priceless "artwork". I have also heard some US English speakers referring to "works of art". So your sentence would sound something like "There are a lot of calligraphy works of art to display". Maybe some other teachers could give their opinion too.