It's not a lie, Taiwan was clearly supporting extraditing him in Feb[1], though there seems to be some concern now[2]

[1] http://www.ejinsight.com/20190213-govt-proposes-revising-ext...

"Taiwanese authorities had asked their counterparts in Hong Kong multiple times to extradite Chan for a court trial, but that has not happened due to restrictions from Hong Kong law."

http://focustaiwan.tw/news/asoc/201902130023.aspx

"Tsai Chiu-ming (蔡秋明), head of the Department of International and Cross-Strait Legal Affairs under the Ministry of Justice, said Taiwan welcomes closer cooperation with other jurisdictions to combat cross-border crime, and he is glad to see Hong Kong's planned legislation."

[2] "Taipei will not agree to transfer of Hong Kong murder suspect if Taiwanese citizens risk being sent to mainland China"

https://www.scmp.com/news/hong-kong/politics/article/3009506...