The 20-year-old's deal at Griffin Park will run until April 27 and he could make his debut against Walsall on Saturday.
Brentford sporting director Mark Warburton told the club website: "Liam is a player I have tracked and monitored for the last two to three years.
"He has come through the same youth system that produced Jeffrey Schlupp, who I am sure Brentford fans will remember.
"Liam has had an excellent academy education and he has developed in to a fine young defensive player.
"He is comfortable both in central defence and at right back and also, crucially, in defensive midfield.
"He has already achieved a lot this season, playing in the Championship with Leicester, and other clubs were looking at him.
"We are delighted he chose Brentford."
Earlier this week Bees manager Uwe Rosler snapped up Charlton striker Bradley Wright-Phillips on loan to further strengthen his squad for the promotion run-in.