Steven Davies' 93rd minute strike forced a replay after Harry Kane and Lucas Moura seemed to have won the tie for Tottenham.
Two fifth round matches have not taken place yet: Rochdale vs Tottenham and Wigan vs Manchester City play on Sunday and Monday respectively.
Lukaku struck very early and finished off wonderful counter-attack to punish the bright but toothless Terriers.
Tottenham have not experienced success in the oldest cup competition in the world in nearly three decades.
Michael Carrick is expected to retire at the end of the season and join Mourinho's coaching team at Manchester United.
Marcos Alonso will be ready to return to action when Barcelona visit Chelsea on Tuesday night, but Tiemoue Bakayoko is likely to miss the Champions League clash.
Harry Kane twisted his ankle and "received some knocks" during Tottenham's 2-2 comeback draw with Juventus in the Champions League on Tuesday, according to Mauricio Pochettino.
Liverpool and Arsenal are out of the FA Cup but the other four from the Premier League's top six are still in with a chance to win.
Mooy suffered a knee injury during Huddersfield's much-needed win over Bournemouth on Sunday (11 February) and could miss his side's next three matches.
Dawson has missed Hull's last two matches with a groin problem while Grosicki is currently struggling with a foot injury.
Scott McTominay was promoted to the first-team by Jose Mourinho last summer and he has backed Angel Gomes and Tahith Chong to follow suit in the future.
Wayne Rooney has suggested that prolific striker Harry Kane will want to leave Tottenham in the next couple of years if they are unable to win major trophies.
Mauricio Pochettino plans to rotate his Tottenham Hotspur squad for Wednesday night's FA Cup fourth-round replay against Newport County, but Lucas Moura cannot make his debut.
Third-tier Wigan's reward for beating Bournemouth and West Ham in the FA Cup is a last-16 tie against Premier League leaders Manchester City, whom they defeated at Wembley in 2013.
Lallana has only made six league appearances for Liverpool this season after being sidelined for a three-month period with a hamstring injury.
Chelsea boss Antonio Conte has claimed that he would like to keep Michy Batshuayi at Stamford Bridge even if the Blues sign another striker before the transfer window closes.
Antonio Conte's side banished the thought of their Carabao Cup exit to Arsenal with a win over the struggling Magpies.
The League Two outfit almost sprung an unlikely cup upset at Tottenham's expense, but they will be happy with a money-spinning replay in 10 days' time.
Antonio Conte has reiterated that the Chelsea board will have the final say on any transfers after refusing to confirm whether Charly Musonda could leave Stamford Bridge.
Chelsea trio Alvaro Morata, Thibaut Courtois and Willian will miss the FA Cup fourth round against Newcastle United due to injuries.
Teenager Angel Gomes could make only his second senior Manchester United appearance in the FA Cup fourth-round tie against Yeovil Town at Huish Park on Friday night.
Liverpool left-back Alberto Moreno may not be ready to make his return from injury in Saturday's clash with West Brom, but has vowed to work hard to dislodge Andrew Robertson.