Werner will join up with the Blues next month after they agreed a deal with Red Bull Leipzig worth in the region of €53 million (£47.7m / $59.6m).
The 24-year-old cannot be registered for the rest of the 2019-20 Premier League campaign, giving Abraham a chance to cement his place as Chelsea's central striker having scored 15 goals in all competitions during a breakthrough season.
Abraham is in talks over a new deal but Werner's arrival could limit his game-time given both prefer to play as a No. 9. Werner can also play out wide but either way, Lampard believes Abraham must accept the challenge posed by the Germany international's arrival.
"I've spoken to Tammy before about the idea of competition and I don't feel the need to have to address every player if a player comes that might contest a position at a club like Chelsea because that's what its about," he said.
"It has been about that in its most successful years in the Roman Abramovich era. And Tammy obviously had a very good season for us this season. He has to sustain and improve on that because at Chelsea we have demands. I am happy to have options and we have options in forward areas and we must have competition for places. So I am pleased with the idea of that.
"Timo is clearly a player that we liked. I certainly followed him myself for a long time individually just as a talented player before I had this job. He's got huge talent, had a fantastic season this year but before that as well.
"Where we couldn't do as much business in the last couple of windows for whatever reasons, it has given us a chance to see some youth have more time in the team but we were very clear we want to improve. Timo Werner is a signing we feel will improve us. I'm very exciting to have him playing for Chelsea."
Chelsea resume their Premier League campaign at Aston Villa on Sunday but will be without defender Fikayo Tomori for 10 days after he suffered a muscular problem in training while winger Callum Hudson-Odoi picked up a knock and is short of match fitness.
"I have sympathy individually with the players to make the decision they see is right for their own needs," he said.
"As a club, we are trying to extend players to stay with us for that period, we will want them to stay. It is well documented a couple of those conversations are ongoing. We have until next week to find the solution hopefully. It would be great for us finish the squad that we started this campaign with and with the quality of players we are talking about."