Liverpool managed to keep Bayern at bay, despite missing their star defender Virgil van Dijk, but could not find the breakthrough themselves despite carving out multiple chances.
The Reds travel to the Allianz Arena next month with it all to play for and Lawrenson believes the fact they did not concede an away goal in the first leg bodes well for their prospects of reaching the quarter-finals.
"Bayern are still a good side and they are well-organised and clever. They had clearly done their homework and made very few mistakes defensively at Anfield, and at the back they read the game very well," Lawrenson wrote in his BBC column
"But they never really looked like getting an away goal, which means there is a good chance they will have to win the return on 13 March to go through.
"If they go on the attack at any time, they have to be very wary of Liverpool's threat on the counter.
"It means the tie is left perfectly balanced. I am sure Bayern will believe the scenario suits them, but I would be confident Klopp's side can go there and score, which is another reason why drawing 0-0 is not the worst result in the world."
Liverpool had their chances to score on Tuesday night but Lawrenson believes they are at their best when they are counter-attacking quickly.
The front three of Mohamed Salah, Roberto Firmino and Sadio Mane were prolific in the Champions League last season, with all three players hitting double figures in the competition.
Lawrenson praised Bayern's defence against Liverpool but he warned the Bavarians about over-committing on the attack given the Premier League side's tendency to strike on the break.
He said: "The reason this Champions League last-16 first leg was so cagey was not down to the Reds. It was because of Bayern's defensive game plan, and how well they executed it.
"I am not expecting their tactics to be dramatically different in the second leg next month but, even if the Bundesliga champions only push on a little more at home, that will suit Liverpool's strength on the counter-attack."