Yes there are many colleges which offer BSc courses lateral entry. You will have to just check which colleges offer it, what is the admission eligibility and process of application. I am pretty sure that there are many colleges offering lateral entry in design courses too. Here are some such colleges:
World University of Design
Manipal University
United World Institute of Design
Pearl Academy
Indian Institute of Art & Design
Lovely Professional University
Here is an article about it. Check it for detailed information: https://design.careers360.com/articles/design-institutes-offering-lateral-entry-admissions

Yes there are many colleges which offer BSc courses lateral entry. You will have to just check which colleges offer it, what is the admission eligibility and process of application. I am pretty sure that there are many colleges offering lateral entry in design courses too. Here are some such colleges:
World University of Design
Manipal University
United World Institute of Design
Pearl Academy
Indian Institute of Art & Design
Lovely Professional University
Here is an article about it. Check it for detailed information: https://design.careers360.com/articles/design-institutes-offering-lateral-entry-admissions