Short answers, pulled from the story.
Matthew Lamb secured a baronetcy for Brocket Hall in Hertford County on the 2nd of May 1755. This event marked his transition from parliamentary service to landed gentry status within a single generation.
Peniston Lamb received the Peerage of Ireland title Baron Melbourne of Kilmore in Cavan County in 1770. The Crown elevated him to Viscount Melbourne of Kilmore in 1781, and he gained Baron Melbourne of Melbourne in Derby under the United Kingdom Peerage in 1815.
William Lamb served as Prime Minister of the United Kingdom during 1834 and again from 1835 until 1841. Queen Victoria relied heavily upon his wisdom and experience during her early reign years while political opponents complained that he had enthralled the young monarch beyond proper bounds.
Historical records suggest it is very doubtful that William was actually the first Viscount's biological son because his mother maintained numerous lovers throughout her adult life. Family historians continue to debate the true parentage of the second Viscount despite extensive archival research into the period.
The entire peerage system collapsed with the final death of the third Viscount Frederick James Lamb who died in 1853. He succeeded his brother William as the third Viscount after William's death in 1848, ending all five associated titles permanently.