On Saturday, he provided a finishing masterclass that impressed Pochettino as Lucas staked a claim for a more regular starting spot, especially with Spurs talisman Kane sidelined for several weeks with an ankle injury.
The ligament damage means the striker will not only miss the rest of Tottenham's Premier League season but will not lead England at June's UEFA Nations League final in Portugal, which will be a huge blow to Gareth Southgate.
"He broke his hand in two parts and it's so painful", Pochettino said.
There was no sign of Harry Winks in the matchday squad for the Premier League clash against Huddersfield and according to the Daily Mirror, it was because Winks picked up a groin problem which forced him to sit out the game.
The England global was substituted with an ankle injury after 58 minutes of his side's 1-0 win over Manchester City in the first leg of their quarter-final tie on Tuesday.
"We need to assess him every day, but we need to have proper answers to see when he can possibly start training with the team".
"They played better than us, it is fair to say, I don't think anyone will disagree", United manager Ole Gunnar Solskjaer said after his side secured only a second win in their last six matches in all competitions. It is so painful, yesterday he saw specialist and today we see how he will deal with the situation.
Pochettino said: "If we assess form since November, he can be a contender".
"We can also confirm that examinations have revealed that Dele Alli fractured his left hand during Tuesday's fixture".
There was no further addition to the scoreline in the first period, but there so almost was two minutes after the break when Juan Foyth clipped a ball in to Llorente in the area, who superbly controlled and shot on the turn but his effort smacked against the crossbar. Pochettino admitted he was unsure whether the England midfielder would face the Terriers: "We need to asses him this afternoon and tomorrow and take the decision".
"I'm more optimistic about him being available for Manchester City in the second leg".