Errani, the 2012 French Open runner-up, is most comfortable on clay, while the 29th-ranked Lisicki likes the faster surfaces. Lisicki, the 2013 Wimbledon runner-up, hit the fastest recorded serve in WTA history (131 mph) last week at Stanford.
Errani was serving for the second set at 5-3 but let the lead slip away. Lisicki next plays Svetlana Kuznetsova or Madison Keys in the $2.44 million U.S. Open tuneup.
American Sloane Stephens used an accurate serve and steady pressure to eliminate Canada's Aleksandra Wozniak, 6-3, 6-0.
Stephens, ranked 22nd in the world, was never in trouble against the 26-year-old Wozniak, who is trying to battle back to her career-high No. 21 ranking after years of arm and shoulder trouble.
''She really played well,'' Wozniak said. ''She served at a high percentage, 75 percent, and it was tough to return.
''It wasn't easy, for sure. You have a warrior mentality, you want to fight for every point, but she played great tennis. I didn't expect that. She played a perfect match.''
Dominika Cibulkova advanced with a hard-fought 6-1, 3-6, 6-0 victory over 17-year-old crowd favorite Francoise Abanda. The Slovak righted herself in the third set and sealed the victory with an ace.
The 10th-seeded Cibulkova takes on Britain's Heather Watson in the next round. Watson edged Tereza Smitkova 6-4, 5-7, 6-4 in a battle of qualifiers.
American qualifier Shelby Rogers downed Ajla Tomljanovic 6-4, 7-6 (5) to set up a second-round meeting with the star attraction of this year's event, fifth-seeded Eugenie Bouchard of Canada.
''I think it will be fun,'' said Rogers, who beat Bouchard in three sets in a lower-level tournament in 2011 in Troy, Alabama. ''Obviously the crowd is going to be for her, and I'm the underdog. I think it's kind of a fun story.
''There's no pressure. I'm just going to go out, play my game, do my best and try to enjoy the moment as much as I can.''
Bouchard, who reached the Wimbledon final last month, is drawn to face defending champion Serena Williams in the Montreal quarterfinals.
The world No. 1 said 20-year-old Bouchard will be a stiff test, if it happens.
''I think she has a really good chance,'' Williams said. ''She's had a stellar year, to be honest.
''She's done better than me in a lot of the tournaments. Yeah, I think it will be a really good matchup. I hope I can get there. I feel like she'll be there regardless.''
Wiliams, coming off a win Sunday at Stanford, has won the Rogers Cup three times when it was held in Toronto, but has not played in Montreal since 2000, when she was forced to retire from the third set of the final with an injury.
No. 15 seed Lucie Safarova, Alize Cornet and Barbora Zahlavova Strycova also moved on. Safarova beat Sorena Cirstea 6-4, 6-2, and Cornet eliminated qualifier Lauren Davis 6-3, 7-5. Zahlavova Strycova ousted Roberta Vinci of Italy with a 7-5, 7-5 win. Magdalena Rybarikova was a 6-1, 6-3 winner over Alison Riske.
After Cibulkova's win, a ceremony was held to induct Arantxa Sanchez Vicario into the tournament Hall of Fame.
The former world No. 1 reached the final of the Canadian Open, now called the Rogers Cup, five times between 1989 and 1998, winning twice in Montreal in 1992 and 1994.
''I know they were great finals,'' the Barcelona native. ''I definitely had to beat Steffi (Graf) and Monica (Seles). They were my biggest rivals at the moment.
''I remember the crowd was always behind me. I feel like at home here in Montreal. As I say, it was one of my favorite tournaments to come and play. In that era, I was probably one of the players that was doing really well in this tournament, and I was fighting to win the trophy. I have great memories.''