I know of a few such shidduchim, but in my experience, you’ll have an easier time getting a litvishe family to agree to a chassidishe shidduch than vice versa. Chassidim stress family background and yichus much more than litvishe do – you’ll find many BT’s and formerly modern litvishe who have no problem getting shidduchim if they are mainstreamed for a significant amount of time and aren’t noticeably different than their peers. Not so by chasidim, by and large.
Also, litvishe girls aren’t used to the strictures of chasidishe life, and likely will not be willing to take on their standards of tznius and avoidance of things like secular books – granted many, many yeshivishe girls are already totally separated from goyishe influence, but a good many aren’t, and are still frum enough to fit into the Bais Yaakov community. Litvishe girls also do not speak yiddish. They also would not take kindly to being referred to as “her-tzi” instead of their name, or sitting away from their husband when there are guests at home on Shabbos.
I’m not saying any of that is bad, it’s just a different mindset, and those differences can ruin a shidduch.