The DS Lite hardware should be similar in specs to the DS Phat hardware, and the differences are largely cosmetic - and all those cosmetic differences would make it an immense pain in the rear end to do, for basically no benefit, unless you REALLY like adjustable screen brightness.
If you're talking about using Lite replacement parts to fix a Phat, that's definitely a no-no. Too many design differences between the Lite and the Phat.