Lossl has six clean sheets this season.
Lossl, a former goalkeeper for the English club, will be on an initial loan from the Danes.
The Bees have an option to make the deal permanent, which would mean a contract through to the summer of 2023 for the 32-year-old.
David Raya is still out with a long-term knee injury.
"Jonas is a very good goalkeeper," said Thomas Frank.
He fits the criteria of what we want in a goalkeeper with his feet and in the penalty area.
In Raya's absence, the man who signed from Spanish side Huesca has stepped up.
Frank said that the Spaniard missed some training recently, with Matt Cox his most obvious deputy.
Lossl played 69 games in the premier league for the Terriers, but did not play for the Toffees.
"This gives us an extra experienced goalkeeper in training and someone who has played in the premier league and will be used to that matchday environment if he starts a game for us," said Frank.
Matthew Benham, the owner of the Bees, holds a majority of the shares in the Danes side.
The outgoing director of football at the Bees is also the chairman of the club.
