Does the A2000 have a graphics card? If not, you'll not be able to use and LCD screen (or any VGA input based monitor for that matter).
The basic A2000 only has a native Amiga RGB output, you'll a modulator if you wish to connect it to a TV using a composite (cinch) connection or using RF modulation (horrible image quality). The best solution for using it with a TV would be an Amiga RGB->SCART connection (if your TV HAS a scart connection ofcourse). I don't know if Amiga shops still sell those cables and neither do I know any schematics :-/.
A flicker fixer makes it possible to use flickerfree interlaced screenmodes on a TV, ie bigger resolution with out interlace flickering. A scandoubler is a device which connects to the Amiga's RGB port and 'doubles' the frequency. The frequency then is ~28kHz (is it?), which is about the right frequency for connecting it to a bogstandard VGA monitor (and with that probably your LCD screen). Be wary that it isn't _exactly_ the right freq for VGA, so picky/older monitors still might not work.
IMHO the best solution would be getting an old graphics card for the A2000 if you want to do some stuff in Workbench. If you just want to play old games you're content with using a TV I'd guess.
