You certainly can revive a lawn on your own. And it should cost a lot less than having a lawn care service do it. With a lawn care service, you're paying for their labor and a profit margin.
A rule of thumb that I use on lawn renovation or replacement, is that if the lawn is at least 50% weeds, you're probably best off killing off everything and starting over from scratch. If fewer than 25% weeds, then weed control and nursing the lawn back to health is the way to go. Between 25 and 50% weeds, it depends on how patchy the weeds are, how persistent the weeds are, etc.
The best time to renovate or replace a cool-season (bluegrass or fescue) lawn is in late summer. If you attempt to do so in early summer, you'll give the weeds the advantage.