She went without necessities to pay for her daughter's lessons.
Literal
She [topic-は] daughter [possessive-の] lesson fees [object-を] pay [purpose-ため], necessities [object-を] without did.
必需品をなしですませた — なしですませる means 'to manage without.' レッスン代 uses the suffix ~代 (だい, 'fee, price'). A sentence about parental sacrifice for a child's education.