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Mouse Drops The Piece.

Some times while I am holding the mouse button down to drag the piece, the piece drops before I lift finger off the mouse . Just started in the last 2 days ... Anyone else had the problem ? Is it likely to be worn out mouse, or poor internet connection ? or Lichess Software ? my speed is 11Mps download & 0.8mps Upload?
mice aren't very good at holding chess pieces. Invest in a cat, they have the paws to ensure that bishop makes it to f6
I cannot imagine how problems with connectivity could cause this. A problem with the mouse seems most likely reason, IMHO. Can you try a different mouse?
If it's a wireless mouse, check the battery.

You can test the buttons for fast double-clicks with codepen.io/blink172/pen/vERyxK for example.
If it shows red, the mouse switch is failing. I've had these issues with Omron switches (D2FC-F-7N 20M) that are common in Logitech mice.

Your best option in this case would be to replace the switch or get a new mouse. It's also possible to dismantle the switch and bend the spring a bit, but this won't hold for more than a few months. There are a few videos on YT in any case. I'd still recommend getting a new switch.