It depends on what sort of "lawn" you are looking for. Many are happy with just a cleared, moderately flat section of turf grasses (usually mixed with a few weeds) that can be mowed to keep tidy and provide a place for kids and pets to play. 'Uneven and lumpy' is not a huge concern unless the hills and divots are significant, in which case you can just fill the indentations to more or less level and seed over.

If you want a smooth, lush looking lawn that is pretty much weed-free, then you should probably start over, removing or tilling in the existing lawn, adding some decent soil and grading and rolling to level and smooth the seed bed before seeding or sodding.

If the second option is your preference, you should probably take this to the Lawn Care forum, as the timing and type of lawn is very dependent on location and the process detailed. Planting a new lawn or rejuvenating or maintaining an existing lawn are not really landscape design issues.

Probably not. It would leave furrows and clods unless you also harrow and roll it. Then you are into reseeding.

How bad is "quite lumpy"? And what caused the lumps.

Possible all it needs is rolling with a pasture roller.

If that doesn't do it, Use a shallow disc or one of those toothy plows on it to loosen the top, then a chain harrow dragged over it to flatten it. Then reseed with a good pasture/turf grass

I have heard that these work ... towed or walk-behind. Rent one?

http://www.everythingattachments.com/Harley-Walk-Behind-Model-W3-with-3-Power-Box-Rake-p/har-power-box-rake-wb36.htm 

I would start with a two by four board and some bags of sand. Fill in the worst holes and level with the board. If the dips aren't deep, the underlying grass will poke through. If not, you need to throw some seed mixed with soil on top and keep it watered (best done during your wet and cool season, usually fall). In other words, try the simplest approach first before you get into renting big equipment. You may have less of a problem than you think. Lawns can be improved over time if you're patient. You will learn where the underlying rocks are, as well as all sorts of other things. Buried oil tanks...septic fields... sink holes.. old patios.. This is the fun!