Wood – How to cheaply refresh parquet in an apartment

We've recently rented an apartment with seriously damaged parquet. Since the deal is "take it or leave it", we've decided to "mend" the parquet ourselves.

Dictionary 🙂 Sorry for my bad english, I don't have appropriate translator for some of these stuff, so I'll use these and here's what I think they mean 🙂
Parquet – wooden floor made of small wooden parts "glued" together
Lacquer – protective coating on the parquet, transparent, (oil based I think)
Emery – rough paper used to "sand" the wood, make it more smooth

The parquet is of relatively cheap kind, the lacquer is completely gone in the middle (leaving the wood exposed and dirty), but there's still some on the edges (about 50% is under lacquer). The proper way to do it is to rent a machine that's removing all of the previous lacquer, flattens the wood further and prepares for a new layer of lacquer. But, we don't want to spend that much money.

Can we just use wooden emery to sand down the parquet that's exposed, and just apply the new layer of lacquer on the whole room? Will the new layer of lacquer stick to the old one or will it fall away when dried? Would it be smart to sand down the previous layer of lacquer just a bit to make it more adhesive to the new layer?

EDIT: The results
First of all, doing sanding by hand is an absolute impossibility – it would take you entire day just to sand out one square meter… So, we purchased the machine for sanding (with circular emery, goes around a cylinder, but with flat bottom) – it's about 30$/40$. But this didn't do the whole trick – because the machine surface is flat, and parquet isn't we couldn't get to the parts that are below the level of neighboring pieces of wood, so we used the drill-mounted-circle-with-emery (or however it's called :)). With all of this, the speed was about 1 square meter per 10/15 minutes. I first thought the lacquer would get hot and sticky and render the emery useless but it really went smooth…(maybe because the existing layer of lacquer was thin, old & worn out).

After that, comes the finishing (lacquer) – we thought about laying out just one layer (to get cheaper) but it just can't be done – the wood "takes in" the lacquer, leaving it dry and not shiny (makes it more difficult to clean afterwards). So, two layers did the trick (with just a "nudge" of sanding in between – it was in the instructions :)), but if you want to get the full effect, 3rd layer would make a difference.

Thanks for the help!