A new mom in the United Kingdom allegedly took time to pamper herself and buy a lottery ticket before taking her gravely injured 7-week-old daughter to the hospital — causing complications that led to the tot’s death at age 2. Sarah Ngaba, 32, admitted to causing “life-shortening and life-limiting” injuries to her daughter, Eliza, and claimed she was guilty of infanticide rather than outright murder, the BBC reported . Eliza died of a respiratory infection at age 2 after a complex skull fracture she suffered after being shaken as an infant, which left her disabled and vulnerable to even simple diseases. Sarah Ngaba, 32, was charged with her daughter’s murder. West Mercia Police At Ngaba’s ongoing criminal trial, prosecutor Jonas Hankin walked the court through Ngaba’s alleged neglect — and abuse — in the hours leading up to Eliza’s hospitalization just seven weeks after she was born.…