Hello Berni,
Lapis can be a tricky material to polish. It is a material with minerals of varying hardness including calcite and pyrite. When using traditional "non-diamond" polishes and laps, it is important to not "overwork". The material and cause pitting from the softer minerals disappearing faster. Push light and quick. Don't sit there with the lapis on the wheel for a long period of time.
The best way to put a quick polish on the lapis is to use diamond. You can use paste or buy wheels af various grits. If there are no large abraded or scratched areas I recommend using a 600 grit, 1200 then a 14,000.
If you only have jewelry equipment, jim has some good suggestions for you. Try the 8000 polish on a rock hard wheel. We have an old automotive polish compound that works wonders also.
Diamond pastes are available relatively cheap compared to the wheels and the equipment to run them. You could even apply some paste on a piece of leather and and work the stone in some cases. The most important thing to remember is not to cross contaminate. Once paste of a certain grit is applied to a piece of hard felt, leather or other material, you can not use that same material with a finer grit.
A great one stop shop for lapidary equipment and supplies is:
http://www.alpha-supply.com
You can find some great stuff there. Good Luck.