With the points shared, Everton has now recorded their fourth consecutive draw while Liverpool awaits their first away victory of the campaign.
Aston Villa bounced back from last week’s first match of the season defeat to beat Everton 2-1 in the English Premier League on Saturday.
Everton secured an important 1-0 win against Chelsea to get a breather away from relegation fight.
Things do not get any easier for Everton, with Chelsea up next at Goodison at the weekend.
Questioned on his relationship with his former employer, Lampard in a press conference on Friday said he is not close to Mr Abramovich.
Cole and Lampard both played for England during their careers and were team-mates at Chelsea from 2006 to 2014.
Everton are 16th on the EPL log, just four points away from relegation zone.
As Chelsea’s manager, Lampard led the Blues in 84 matches in all competitions, won 44, drew 17 and lost 23.
Rooney’s ties to Everton run deep. He joined the club as a nine-year-old and made his first-team debut aged 16 in 2002.
Mr Smith, who formerly led Aston Villa, is expected to resume with his assistant, Craig Shakespeare.
