Those 2 stroke engines are problmatic and require too much work to keep them running. Consider switching to a more reliable 4 stroke Briggs if mowing lawns is what you are really interested in.

Does the smoke get worse the longer you run it? If so oil is getting past the rings.

'Does the smoke get worse the longer you run it? If so oil is getting past the rings.'

Please - it's a 2-cycle.

This smoke indicates excessive oil is being burned because: there's either too much oil in the fuel or too much fuel mix being burned.
The mix ratio is 32:1 with Lawn-Boy oil, or one 8oz can into 2 gallons of regular gasoline.
If the mix is right, the first thing to check is to make sure you are pulling the throttle lever back off of choke after the engine starts and putting it in the 'fast' position. Now take off the air filter element and make sure its clean and oiled. While its off, look in the carb to see the throttle plate connected to the air vane shaft - with the engine off it must be in the wide-open position. Shine a light in and have someone work the throttle lever to see if the choke plate is opening when you pull it off choke. If everything is good so far, chances are the float is stuck or not set properly, allowing uncontrolled fuel into the engine. Pick up the rear end of the mower about 6" off the ground and drop it a couple times. Start engine and see if it straightened out.
Orangedot's advice on the fuel shut-off was good. Particularly if it smokes on start-up but runs normally later. This means fuel is leaking down into the engine after putting the mower away. It can fill up the exhaust transfer pipe and get blown into the muffler when starting, which takes awhile to all burn off.
As for the other problems, they are pretty typical. Always have a new coil pack on hand and a new carb, at least the body and float.
Once it's running cleaner, check the RPM. If less than 3200, you can speed it up by turning the knurled collar at the base of the air vane 4 clicks clockwise. Do this and then mow with it for at least 10 minutes. You can do this a few more times if needed - you can't over-speed the engine. You can find out what the engine will do wide open by just pushing the air vane all the way over with a small stick and holding it. Assuming it has the correct blade in good condition and a mulch fan, the engine won't be able to go much above 3600 RPM.

Saxman's advice is good. I'll add that the oil on the deck under the muffler sounds like fuel is leaking into the engine when the mower isn't in use. Consequently, adding a fuel shut-off valve should be the first thing you try.

Welcome to the joys of owning a 2-cycle Lawn-Boy. They're good mowers, but the carburetor and CD pack issues get old after awhile--which is why I now own a 4-cycle Toro.

Thanks...must have been the fuel leaking past. After 15 or 20 minutes it finally started clearing up. The ratio was dead on correct. Had 2 gallons of gas and one can of LB oil...I was anal with the gas station to make sure he had exactly 2 gallons. This mower has a fuel valve, and I never turned if off. Will start doing that from now on.

Throw 2 to 4 oz of Marvel Mystery Oil into that mix and the engine will gradually clean up. This is in addition to your mix oil.