The handle mechanism contains a small tab inside to stop and align the handle in correct upright position. This fails when the tab is broken or worn.
A handle replacement is needed when the handle wont come back by itself. If you can not find the right handle, you need replace the complete handle mechanism.
The process is by removing the lid from the tank, followed by unhooking the chain and unscrew the small nuts inside the tank. Remove the handle mechanism out from the tank. Replace the handle mechanism by unscrewing the handle or if required replace the entire set.
Replace the working handle mechanism back to the tank and screw the nuts back on the handle from inside. Reattach the chain and check the toilet if it works good by flushing. Put back the lid on.