My cub cadet modle LT1045 doesn't seem to be getting gas. The fuel filter looks clean. If I spray gas directly into the carb it runs fine but as soon as I stop it dies.

"runs great" is subjective. Likely all it needs is a valve lash adjustment.

Kohler SV710 0.005in. +-.001

clean the fuel jet hole out with a fine wire or air compressor.

First, is there an on/off valve for gas flow? If there is, make sure it's turned to on. It's easy to forget that you've turned it off, especially after the mowing season has ended. Second, if gas is getting out of the tank to the fuel line, you might want to look at the fuel pump. You can disconnect the fuel line coming out of the pump and see, in that couple of minutes it runs, if the pump is actually pumping fuel. If it is, then you've got to think carb - although if it's relatively new, the chances of having a bad carb are small. Is the gas old? You might try draining the tank and refilling it with some high test gas, or even better, some ethanol-free gas if you can find it near where you live. I always use high test and add a couple capfuls of "Sea foam". You can get that at any auto parts store.

Obviously, you want to make sure the air cleaner is clean. As a last resort, you may want to spray some ether in the throat of the carb and see what happens - although YOU MUST NOT SPRAY TOO MUCH LEST YOU BURN IT UP!!!

If none of these measures work, take it to the shop. Cub Cadet is not the quality machine it once was, unfortunately. I had one briefly and wound up selling it and buying a John DeereX300.

You might want to try using a carburetor cleaner additive, or a spray cleaner to clean the carb internally. Make sure your air filter is clean. You may also want to make sure fuel lines are not restricted.

Have you tried putting a little gas down into the carburetors throat ? If it starts then you'll know you're dealing with a fuel delivery problem. You claimed you have spark so I'm assuming that it's a good blue color, I think if it was me I would be pulling my flywheel off and checking to make sure it hasn't sheared or moved. If you were able to rule out the fuel delivery issue.

Get rebuild carb kit change float and all jets with new

Are you pulling the plug to check for wetness after cranking it a few times, WITHOUT using the starting fluid? Also, I would recommend using carb cleaner in place of the starting fluid. Starting fluid runs the engine VERY hot for a brief time and can possibly damage rings, valves, and aluminum parts.

coil

try and run it with the gas cap loose maybe the vent is plugged

A defective fuel shutoff solenoid under the carb bowl or a carb that needs cleaning/repaired.