The 21-year-old has hit the ground running since joining Boro at the start of the season, scoring 13 goals in 13 Championship appearances. He is the division's leading scorer and has found the net in five consecutive matches, helping his new club climb to the top of the table.
With Middlesbrough emerging as genuine contenders for promotion to the Premier League, Lankshear's form is attracting attention well beyond the Championship.
His progress has also prompted speculation over whether Spurs might regret allowing him to leave.
As part of his transfer, sources indicate that Tottenham secured preferential terms should they wish to bring Lankshear back. That provides a potential route for Spurs to act if his development continues at this rate.
However, Tottenham insiders insist there is no current direction of travel towards exercising that option or any expectation of an attempt to bring him back any time soon.
That is perhaps unsurprising given how recently the club sanctioned his departure and the significant opportunity he has been given to establish himself at Middlesbrough.
Lankshear signed a five-year contract at the Riverside Stadium, with an initial fee understood to be around £10million. Performance-related add-ons could take the overall package closer to £20m.
Tottenham are nevertheless looking to add more firepower to their attack and would like to bring in a striker during the January transfer window if the right opportunity emerges.
Lankshear's form makes him an intriguing name to keep in mind, but for now there is no expectation of a swift return.