Lx425 has grinding noise but won

Have the battery load tested (any auto parts can do this for free) and make the engine spins freely.

First make sure your battery is fully charged. The charger on lawn tractors will not keep the battery fully charged as they just produce a light charge. Check battery before the starter but if battery is fully charged then it's possible the starter could be bad.

solenoid on starter motor .

A whinning noise is usually from the starter spinning but not engaging with the flywheel.
The solenoid or bendix gear may not be working which would require a replacement starter.
If you heard a grinding noise, I would say some teeth are missing from the flywheel.

Belt Length of Toro LX425

Deck Belt for Toro LX420 LX423 LX425 LX426 LX427 1125800 112 5800 Made In...

The grinding noise is the starter hitting the fly wheel. This means that the starter is spinning but may not be engaging all the way. Your Flywheel is probably missing a few teeth now. I recommend replacing starter and flywheel. If you're on a tight budget then you could just replace the starter but it will cost you more in the long run.

The transmissions gear is bad need to replace

You can go to Toro.com and look at the lower left side for "Homeowner" or "commercial" parts. If you enter your model number you can get an owners manual online. I tried your LX425, but didn't come up. Maybe a different number?

Yes apply some heat and it will break it lose and the system will spin just fine