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."