She spared no effort to go pick up her friend at the airport.

Literal

She [topic-は] effort [object-を] not-sparing airport [toward-へ] friend [object-を] to-meet went.

労を惜しまず (ろうをおしまず) is a literary expression meaning 'without sparing effort.' The ず ending is the classical negative form of 惜しむ ('to begrudge'), functioning adverbially — a survival of classical Japanese grammar in modern set phrases. 迎えに行く uses the purpose-に + motion verb pattern.