A few things to get out of the way...The F-series boxes, and G-series boxes are interchangeable...at least on the FS engine, but that should basically mean any F series equipped block will accept a G series straight up. Some Australians had mounted a JDM FS-ZE (which uses a G series box) into a FP 1.8L protege, and used the F series box from the FP...but the F series are weak apparently, go with a G15 if you have access to it.
If the donor is a protege, and not a miata...you shouldn't run into the intake manifold being 'backwards'...I'm not overly familiar with this swap, but just make sure you have room for the intake and exhaust plumbing obviously...
then its down to the mounts and axles....both of which can be custom made if need be....you'll need the half shaft from the BP protege (unless the 1.6L bolts to the BP engine properly), and axle wise...it will be dependent on any differences between the outer CV joints spline count and diamater...I don't know what the 1.6L uses axle wise...but a G15 is whats in all 3rd Gen 2.0L proteges...so axles from that will fit, as long as the box is oriented in the bay at the mostly the same place...and the other end will be the knuckle/hub...you may have to basically fit a 2.0L 'sport suspension' to the front of your 2000LX to use those axles for the G15...I don't know if the stock 1.6L hubs are the same.
the F and G series boxes mount the same way in a 3rd gen protege (the 1.6L and 1.8L 3rd gens both used the F series, the 2.0L's used the G series)...i'm not positive the mounts themselves are the same, but they mount to the same section of the front sub-frame. If you're using the F series from your BJ protege, this isn't an issue...if you're using the stronger G series from the BP, you may have to find a G series driver's side mount from a 2.0L BJ...The other 3 mounts, can't comment. You'll have to determine if the timing belt mount, the 'rear' mount under the intake manifold, and the front mount fit properly...it would be a good idea to source some used or even destroyed mounts from other members, or a junk yard, for cheap to see what modifications...if any...are needed.
BP's are fantastic engines...with bottom ends that will hold for hundreds of thousands of miles...or very heavy boost (or both in a lot of cases haha)...so it would be cool if you get this to work...but its a very uncommon swap, so you'll be doing a lot of the measuring on your own i'm afraid.