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Monckton is the daughter of Marianna Laetitia Bower and Gilbert Monckton, 2nd Viscount Monckton of Brenchley and was educated at the Ursuline Convent at Tildonk in Belgium.
- The Hon. Timothy David Robert Monckton (born 15 August 1955)
- The Hon. Jonathan Riversdale St. Quintin Monckton (born 15 August 1955)
- The Hon. Anthony Leopold Colyer Monckton (born 1960)
She is married to the journalist The Hon. Dominic Lawson (brother of the food writer Nigella Lawson). They have three daughters, Domenica, Savannah and Natalia (deceased). Domenica has Down syndrome: her godmother was Monckton's friend Diana, Princess of Wales.
In 2017, Monckton wrote a controversial piece for The Spectator arguing for learning-disabled people to be able to work for less pay than minimum wage, citing 1.3 million unemployed people of 1.4 million people with learning disabilities in the UK. This article was criticised by members of the disability rights movement.
Rosa Lawson is a fundraiser and supports several charities relating to children and Down syndrome. The charities include:
- The Acorns Children's Hospice for the care of life limited children in the heart of England
- Downside Up a Down syndrome charity in Russia
- The Down's Syndrome Educational Trust based in Portsmouth, England which through research provides education, information and training to promote the development of children with Down syndrome
- Kids (charity), a disabled children's charity based in England. KIDS helps in developing and improving the lives of disabled children
- The Bulgarian Abandoned Children's Trust, a British charity dedicated to helping disabled and disadvantaged children in Bulgaria and campaigning for an end to the use of institutional care
- Team Domenica, a charity named after her daughter which supports young adults with learning disabilities to find employment
Lawson was awarded a Member of the Order of British Empire in 2017 Birthday Honours List for voluntary and charitable services to People with Learning Disabilities and their Families in the UK and Abroad.
- 'MONCKTON, Hon. Rosa(mond) Mary, (Hon. Mrs Dominic Lawson)', in Who's Who 2011 (A. & C. Black, 2011)
- Monckton, Rosa (4 March 2017). "Why people with learning disabilities should be allowed to work for less than the minimum wage". The Spectator.
- "Rosa Monckton: Let learning disabled work below minimum wage". BBC News. 2 March 2017.
- "Our Story". Team Domenica website. Retrieved 29 June 2019.
- The Daily Telegraph: A helping hand for struggling parents. - Interview from 28 September 1999
- The Daily Telegraph: I will talk of my daughter in English, not Newspeak - Interview from 16 May 2004
- Daily Mail: My Down's daughter keeps our family together. - Interview from 4 November 2005
- Daily Mail: My Down's daughter changed my life - 14 November 2007