Regular tools for the most part are fine. I cut sheet on a delta X5 10" table saw (52" beisy fence cause' hell yeah, it's heavy). Sheets can be laminated together seamlessly but it take a lot of practice. I use all different router bits from cheaper Bosch to Whiteside, so regular old router bits work fine. Again on the type of material you are using: You said you have Lucite, do you know which type? Does it still have the paper on it? Possible Lucite E, LL, or GP? This plays a HUGE factor in how you work with it as Extuded materials are not as dense as Cast and have a much lower melting point.
On the table saw I use a High tooth count (110) triple chip carbide blade to eliminate blade melt and get a smooth cut. Though if you are cleaning with a router after it doesn't matter as much.
HTH,
R-