Hundreds of people have left their condolences on a special Facebook page set up in tribute to the family that died in a head-on collision near Grimsby.
More than 33,940 people joined the R.I.P Cockburn Family page on the social networking site within a few hours.
One person posted, "So so sad xx dancing with the angels now x R.I.P xxx".
Another left a message that read, "Dance in heaven beautiful angels x".
Many left anecdotes about the family on the page, with one describing Mr Cockburn as "a gentle kind man" who was "totally devoted to his family".
A number of people also posted tributes on Bethany Cockburn's personal Facebook page, on which she described daughter Lacie as "Our world!".
More top news
Ex Army chief calls on Government to "think the previously unthinkable" and consider sending ground troops to combat Islamic State.
Rio Ferdinand has described being "overwhelmed" by the support he received from football fans after his wife died.
The world's oldest-known person, Jeralean Talley, celebrated her 116th birthday with family and friends at a restaurant in Michigan.