Engine RPM run away

Without cranking it, can you take the air filter off and see the throttle plate move as the throttle is moved ?
If someone else cranks it, can you be at the carb and move the carb throttle directly at the carb and control the rpm ?
If so, check your throttle rod for slack, missing spring/connection, something broken.
Sounds like the carb has nothing stopping the throttle from being sucked full open.

Hi Roger:
What kind of engine are we dealing with?
Maximum RPM is limited by the amount of load imposed on an engine. No load lets a 1 hp Briggs and Stratton scream at 6000 RPM when you bypass the governor, or your weedeater with no line sound like a ninja race bike. Add some load and they both slow way down.
So, reply as a comment to this post and we'll try to figure out what can be done for your circumstance.
Cheers.

There are several possible Mowers of the "L" 155 versions.
John Deere LA155 garden tractor lawn mower. These stopped being made in 2010 (they started production in 2009, and so enjoyed a run of 2 years on the assembly lines). The JD LA155 is powered by a Briggs and Stratton 2 cylinder, V twin engine. This engine is 0.656 liters (40 cubic inches) in size and produces 22 hp.

1998 - 2001 LT Series
John Deere LT155 Engine: Kohler 1-cyl gasoline

2006-2006 L155c, This series was produced only in 2006.
Briggs & Stratton gasoline, 2-cylinder air-cooled, 724 cc [44.2ci ], 25 hp

Model 445777-0168E Code 021125YC, these are the engine numbers from a 25 hp twin cylinder, B&S.

Notes on these engines from parts supplier ereplacementparts.com:
Briggs and Stratton 445777-0231-E1 Engine: The proper flywheel part number and/or the alternator magnet size will determine the alternator type or output.

This 25 hp engine has 3 different possible alternators, standard circuit, dual circuit, tri-circuit. I would need the exact engine model numbers in order to precisely answer your question. Often mower models have choices for the engine they come with. In this situation the engine model is more important than the model of the mower.

Testing an alternator is fairly simple; all you need is a multimeter for testing.

1. Disconnect connector from stator.
2. Set multimeter for AC volts.
3. Attach RED test lead to either pin on stator side of stator connector. (On single wire leads, attach RED test lead to the single pin.)
4. On two wire lead models, attach Black test lead to the other pin. On single wire stator connectors attach the Black test lead to the engine ground.
5. Prepare the lawn tractor for engine start (set parking brake, blade off, etc). Start engine and run at full throttle.
6. Check output. Output for engines of this general size run in the 30 to 50 volt range. For instance the B&S V twin 22 hp AC output at full throttle is 30 Volts minimum. Other B&S on these machines spec 40 Volt minimum.

If your voltages are not in the manufacturers range, or non-existent, your stator is partly shorted or completely burnt out (open circuit). Either way you have to replace it.

A. In the picture is a single lead stator connector.
B. In the picture is a two wire stator connector.

Check the idling setting screw is not holding open the throttle butterfly common fault to fix if the engine races esp when no load is applied the idle throttlexpostion is to high thus the engine runs faster at idle turn the screw located on either the butterflyistelf so less screw threes is against the carb body this should start lowering the idle speed of the engine it should be around the 900 RPM approx for idling and top rev of 3500 at full throttle a rev counter is displaying a extra high rev count the it's the oil governed at fault or malfunctioning or sticking this will cause and engine to race badly to the point of engine destruction eventually
You may need to adjust the movement of the governing leavers etcetera best done by qualified servicing personnel a lawnmower mechanic etc

This can happen when extra air is entering the engine. If you have a vacuum leak the engine will race because it is like the throttle is open further than it actually is,

You can try using a water spray from an old spray bottle and when the engine is running, spray along the gaskets, vacuum lines, and switches until something changes your RPM. Then you would have found the leak,

Now on some engines a part called an ICS, or idle control solenoid is in the intake manifold and it has valving which can get stuck. Removing this part and cleaning with WD-40 can help. Use the Web to get a picture of the ICS for your year and model. Google with those terms to get helpful info.

While your car is running.......pop the hood and find the throttle body. The throttle body is where your air filter tube/hose goes to the engine. Locate the throttle position sensor which should be on the side of the metal throttle body. This should be the item causing this. If you grab the plug that is on the sensor and wiggle it while the car is running then the engine should rev and act up if thats the problem. If not let me know and I can direct you further. Thanks.

You do not have a problem. Air cooled small engines are designed to be run at full throttle in order to mow correctly and to cool the engine properly. Running it as less than full throttle will cause the engine to overwork and possibly overheat thus shortening it's life. It will also not cut properly as you have found. The engine has a governor that prevents you from running it too fast. Run the engine at full throttle at all times when you are mowing which is the optimum speed for proper operation. You may think you are helping your engine by running it slower but in reality you are harming the engine. It is air cooled, not water cooled, and needs the revolutions in order to cool itself properly. Also use 100% synthetic oil in this air cooled engine for more protection. Change your oil/filter once a year or every 50 hours.

You may simply need a new fuel cap,vacuum in the tank will rob your fuel and stall it engine,try taking off the fuel cap and see how it runs.If this does not help you may need a new fuel pump,which runs off of crank case pressure and should take over from the choke once the tractor has started.

Have had to replace fuel line in tank MANY times do to it being split just above pump.Try doing a fuel pressure test on the return hose from throttle body,should be close to at least 40psi.

Check the seat switch for the running problem. Disconnect the switch and jump the harness with a piece of wire, and see if the tractor stays running. If so, then the switch is bad. As for the charging problem. Test the voltage regulator. Start the tractor and put a volt meter across the battery. Red to red and black to black. Run the RPM to full throttle. You should have a reading of 14 to 14.5 volts. If not, the regulator is bad. Hope this helps.