Hot-shot Lankshear, 19, is one of Spurs' brightest prospects and an England youth international. The Baggies won the race for his loan signature until the end of the season on Friday.
The England under-20 international is a much-needed natural centre-forward option Albion have lacked for some time in the absence of the injured Josh Maja.
Mowbray's men put five past Portsmouth two games ago but struggled to break down bottom side Plymouth on Saturday and were overcome for a frustrating 2-1 defeat.
Lankshear, who has made six senior appearances and scored one goal for Spurs, was not involved against Argyle and can make his debut at home to Sheffield Wednesday next Saturday.
Mowbray said: "I remember sitting to watch the Galatasaray game where he scored early and got sent off late on - he's a young guy, probably trying too hard that night and got two yellow cards.
"He's played at a really decent level, scored goals at the age group, let's see how he does. To be honest I've had some amazing loans and first loans that need a second loan, they're moving away from the comfort of their own environment, coming somewhere different, living on your own for the first time, not knowing anybody. Let's see how he adapts."
Albion have started without a natural striker for the last couple of games with winger Jed Wallace and Grady Diangana, a wide or central attacking midfield player, leading the line.
The head coach has enjoyed success nurturing youngsters who have gone on to be high-profile Premier League talents and Albion are hopeful Lankshear could have a similar path.
"Of course I'm pleased. I've had some success over the years with Premier League loan players, I would suggest," said the head coach. "(Amad) Diallo and Harvey Elliott as attacking players - and Adam Armstrong.
"I've spoken to Will. He's got some physicality, he knows where the back of the net is, he's just creating competition for the squad and hopefully he can come in and help us."
Albion have until 11pm on Monday to complete any final business before the transfer deadline.
The Baggies also saw loan midfielder Uros Racic return to his parent club Sassuolo before heading out to Portugal outfit Braga on loan.
The club were content for Racic's loan to end after the Serb's disappointing half-season saw him drop down the pecking order. It is understood Albion will not seek a replacement.
Mowbray said: "I think he was finding it difficult that he wasn't involved, wasn't starting, in my first two weeks here.
"I did have a good chat with him. He's going to Braga, amazing, good on him. Everyone has their own personality.
"He was frustrated, disappointed, he wanted to play, I was saying I'm just in the door and you're not in the team, I've watched you in training and the bottom line is my decision is you're not going straight into the team, I'm taking somebody else. Himself and his advisors wanted to move on and that's fine, no problem."