It just happens that my LA145 has had this problem on and off for the last month. One time I got around it by disconnecting the fuel cutoff solenoid connector and repeatedly plugged it in and removed it to cause the solenoid to rapidly energize/de-energize. One time I removed the fuel line going from the fuel pump to the carb and blew into the end of the hose. Another two times, I choked the engine completely with my hand over the intake so that there was much more suction than just the carb's choke. If you see a pattern here, its that fuel feed to the carb is the issue. I had plenty of fuel to the bowl, but there was no fuel getting jetted into the intake manifold.
This morning as I started to mow, the mower just died and refused to start with any of the above methods or coaxing. Like you, if I dribbled a little gas into the intake, the engine fired and ran perfectly for a few seconds. I decided it was time to "operate" on the carb and find where fuel flow was being stopped.
Removing the hood is a snap on my mower. You just open the hood, lift up, and pull forward. The complete hood comes off and you can put it out of the way. I did have to disconnect the connector for the lights.
My engine is the B&S 22 HP engine. Removing the float bowl is not possible (or not possible for me) without taking the entire carb and intake manifold off the engine. I did have to lossen the top cover/cowling on the engine as well before removing the carb/intake so I could get to the 3/8" bolts that hold the carb and manifold onto the engine. The bolts also have a star socket that makes it easy to use a nutdriver to remove them. I didn't need the 3/8" open end wrench on any but one of the four bolts. The intake manifold is plastic and has metal bushings around the holes so you will not crush or crack the plastic, but do not over-tighten when reinstalling. There is one additional screw on top of the carb under the air filter that needs to be removed. The choke linkage and the accelerator linkage are pretty straight-forward. When you remove the intake, you will notice they have o-ring seals between them and the engine head.
With the intake and carb removed, I first removed the triangular plate on top of the carb which allows access to the fuel orifices. I saw no trash there and was able to just put that cover back in place since the gasket was not damaged at all when I removed the plate. Next, I flipped the whole assembly over so that the float bowl is exposed. The float bowl has no drain and the fuel cutoff solenoid is on the side of the bowl. The bowl is heavy cast aluminum and made very well. It is held in place with two screws that are combo phillips/slotted. This proved to be the toughest to break loose. The screws are very tight and my phillips screwdriver slipped and burred one of the screws. I got a large flat blade screwdriver and was able to unscrew both, but with a lot of effort.
As I removed the float bowl, I noticed it also was sealed with an o-ring and it was not damaged as I took the pieces apart. The bowl has a large bowl around a smaller round fuel-feed sump. The fuel cutoff solenoid opens a passage from the large bowl to the small sump to allow it to fill with fuel. The top of the float chamber has a nylon pickup with two jets that sits down over the small sump and seals with another o-ring. When fuel is available in the sump, it is drawn up inside the pickup. The nylon pickup can be removed with two screws and lifted up to reveal two brass feedpipes going upward to the feed jets that are under the aluminum triangle piece on top of the carb.
The float is plastic and nothing abnormal about it. The needle has a rubber tip that seals the inlet when the bowl is full.
My bowl had black specks in it that looked like residue from gas drying up or some manufacturing dust. I cleaned it out and backflushed all passages. I didn't use any high pressure air or cleaners. I just used clean fuel. I was afraid to use chemical cleaners that might damage parts or seals. I blew through passages with my mouth and everything seemed to be clear. I manually moved the fuel s/o solenoid and watched fuel flow from the outer bowl to the pickup sump. I even hooked the solenoid up to its connector and turned the key on and off to watch it operate. It worked perfectly. I also removed the float and needle and made sure it was all clean.
In reverse order, I reassembled the whole carb and intake to the engine. I poured fuel down the hose until the bowl was full and inspected for leaks around the float bowl. All was good. I put the hose back onto the fuel pump and re-installed the hood after going over the engine to make sure all is okay. There is one crankcase breather hose that attaches to the back of the intake that you need to make sure gets re-connected.
There was nothing out of the ordinary with this whole job. It was pretty easy and straight-forward; just a good float bowl cleaning that required the whole intake be removed. I can't say for sure what was being stopped up, but when I spun the engine over, it fired right up and ran perfectly while I mowed this morning. I can only assume that something was clogging the intake or maybe sticking the fuel s/o solenoid. Whatever, my LA145 now seems to run perfectly and I know all that trash is out of the carb bowl.