What kind of oil do I use for a troy built lawnmover?

If you look on th edipstick it may tell you there. If not try the owners manual if that does not work MOST are good with 5-30 or 10-30 oil.

Straight HD-30 (high detergent) above 40 degrees F
10w-30 and 5w-30 conventional below 40 degrees F
OR 10w-30 and or 5w-30 synthetic all year round...

Using a conventional multi weight will in fact sometimes make them use oil... as it does thin out under the high heat these things put out... while syn does not.
Straight 30's OK... just not in the cold temps, you can and will damage the engine starting a engine with a straight weight...
Check the oil often, and change it every 25 hours.