Any search tool for LXDE menu?

Forget about that, there's nothing like that for the LXDE menu, use Synapse.

Install it from the terminal: sudo apt-get install synapse

Synapse review with screenshots http://www.omgubuntu.co.uk/2010/11/synapse-gnome-do-launcher-app-review-ubuntu

The correct, fancy name for it is semantic launcher BTW :)

Other related stuff:
Zeitgeist - indexing tool used by Synapse
Gnome Do - another launcher similar to Synapse, older

Kupfer provides a simple menu searcher activated from a global keyboard shortcut.

sudo apt-get install kupfer

By default you show Kupfer using the global keyboard shortcut Ctrl+Space.

https://kupferlauncher.github.io/

A quick video review can be found here.

XFCE provides an excellent app finder. You can install it with

sudo apt-get install xfce4-appfinder

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