Car has a bad ideling. When car idels and u try and remove the oil cap car cuts out.What can be wrong .

Vacuum leak. check all vacuum hoses to ensure they are connected and not cracked or damaged.
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You probably have worn main bearings and worn cam bearings try a can or two of STP also would be nice to know what car and engine to better advise you .

You don't add oil with the car running

You broke the vacuum for the crankcase evacuation
(PCV System)

If you have idle problems then they have to be diagnosed

When the oil lamp lights, it means that your oil pump is not giving the right pressure or it is not working, If it only happens during idling, it indicates that the pump is about to wear and needs servicing, If its intermittent, it may just be a loose wire connection to the sender or a defective sending unit. Try to replace first the oil pressure sending unit.

Could be a few things......low motor oil, clogged oil filter, bad oil pump, clogged oil sump (pick up tube), idel too low....ect...Hope this helps ??

These cars tend to have bad spark plug wires, they will arc where the boot goes down into the valve cover.Check to make sure there is no oil in the spark plug well,if the is you will need to replace valve cover gasket and orings.Souds like you need a new set of plugs and wires.Look for corosion where the wires connect to distributor also as you may also need a new cap and or coil.

Check for vacuum hose off, broken,cracked, or loose at a connection.

Most Lesabre have the 3.8 engine. The engine has a device called an automatic idel speeed motor or AIS for short. It's held on with two torx 20 screws and a 4 wire electrical connector on the side of the Throttle body. BUT BEFORE YOU GO REPLACING THIS DEVICE THAT CAN COST OVER $50. Try this first. Don't drive the car around this way just test it! Remove the big vacume hose from the power brake booster and put your finger over the end of the hose going to the motor. Have an asstant start the car and hold the gas so it'll keep running, trying to go as slowly as they can. Slowly remove your finger from the end of the hose and the motor should pick up speed. you should be able to get a good idle with your helper completly of the gas. if you do the idel motor is'nt working ( right) so your not done checking. Let's say you can't even get a fast idel that stays. The timing chain needs checked and other vacume or engine control codes need checked. Has the check engine light been on? ( with the engine running) . If it has the idel motor will set a code as will a cam senser and all the other sensers on the car. Follow code charts if a code is found. Most auto parts stores will check your car for free for codes but their recomendations very with the experience for the operator of the tool, and if they were good enough to make the mechanics money why are they in a parts store? If you can acheive a good idel playing around with the vacume hose then put it back on and go to the next step. Remove the Idel motor and clean it and the hole it came out of with oven cleaner. Just like cleaning an oven don't get it on you or the wiring part of the motor. With an OHM meter the pins will show two different pins hooked together ( two Pair) If you get only one it's bad. Every pin is connected to just one other pin. If not it's bad. You can get new cheap ones that are bad. I use cheap ones and cross my fingers. If they work the first time their good for a long time. Then you have to learn the idel. Try to learn the idel with the old one cleaned first. Start theengine and hold the idel with the gas pedel. after holding the speed at 2000 Rpm for two minutes ( a good engine will do this easy) let off slowly it should idel down slowly then (catch) and speed back up on it's own. If it does your fixed and go on your merry way.

sounds like dirty injectors......

Check water pump or bad radiator there is a circulation problem. As a last resort check and make sure its not a bad head-gasket check oil for antifreeze look under oil filer cap for cream-ish white residue. Good Luck