Since Laravel is a server-side technology, you would probably want some sort of javascript library to achieve that functionality--unless you're willing to use forms that look like tables or tables with form elements inside them. You might also have some luck with contenteditable attributes and events. HTML doesn't have an editable form out of the box that automatically interacts with the backend (Laravel in your case).
It depends on what you want to use the tables for; if your tables have a lot of data, you might later want sorting or pagination and that's something javascript table libraries are useful for.
If your tables are simple or exist mainly for style purposes, you might be able to get away with not using javascript much or at all. It would be fairly unusual to go this route, though, and probably take a little longer to get a working prototype.