We know the Lao Tian Li studio continued into the early 1920s, because Jin Shiquan 金世权 at age 12 was apprenticed there in 1922 under senior craftsman Liu Guangde. Was Lao Tian Li himself still alive then and overseeing the studio? This interesting vase has a rare combination of stamps on its base - the signature stamp of Lao Tian Li, plus a "MADE IN CHINA" stamp. A country of origin stamp including the words "Made In" was required to be on products exported to the United States after a 1920 tariff act - previous to that, only the name of the manufacturing country was required. The stamp is a stylized version of Lao Tian Li's engraved signature that appears on earlier pieces.
UPDATE: A following blog post comparing this vase with another piece in the lotus pond theme that seems to have been made for U.S. export: