The teams clash in the Premier League on Monday before reconvening for an FA Cup fourth-round tie on Sunday.
While their first cup encounter for almost two decades will stir memories of their Wembley showdowns in the 1980s, the local rivalry is not as friendly as it used to be.
After last season's Anfield derby, Liverpool manager Rafa Benitez criticised Everton's supporters for a tasteless chant about captain Steven Gerrard's daughter.
Benitez had also got in on the act 12 months earlier by describing Everton as a "small club".
"The whole city moved itself to north London for a day," Lawrenson told Reuters.
"You just saw Blues and Reds together everywhere. People tell me it's not particularly great any more but in those days it was just fantastic banter and both sets of players got on very well."
"I don't think the rest of the country could understand that," added BBC pundit Lawrenson, who played in the 1986 FA Cup final which Liverpool won 3-1 a week after pipping their neighbours to the league title.
Sharp said: "Everybody came together, there was none of the bitterness seen now. When we went on to the pitch we wanted to beat them but we still remained friends."
Lawrenson said: "I believe they should share one stadium. That is the way forward."
There are different reasons for the souring of relations. The fortunes of both clubs dipped in the 1990s, although Everton's more markedly.
Soccer's increased popularity also makes it impossible for fans to make a last-minute decision to watch a derby game, meaning fewer Blues and Reds sit together.
Everton came from behind four times, with Sharp netting twice. "I don't think there have been any to beat that one," he
