Just assign the lodash function directly as a component method
new Vue({
    el: '#app',
    data: { requests: 0 },
  methods: {
    search: _.throttle(async function () {  
      const res = await fetch('/echo/json/')
      this.requests++
      console.log(res)
    }, 1000)
  },
  created () {
    // 100ms interval but throttle works at 1000ms
    setInterval(() => {
        this.search()
    }, 100)
  }
})
https://jsfiddle.net/6thcxfym/
In your case:
methods: {
    search: _.debounce(async function () {
      // this code may differ from your actual implementation
      const res = await api.get('/users/')
      this.options = res.data
    }, 1000)
  }
}