Both sides of the lake are exempt from the tax.
See link below for details...
https://www2.gov.bc.ca/assets/gov/taxes/property-taxes/publications/is-2018-001-speculation-tax.pdf
The tax applies in the Metro Vancouver Regional District (excluding Bowen Island and
Electoral Area A, except the part of the electoral area that is the UBC and University
Endowment Lands), the Capital Regional District (excluding the Gulf Islands and Juan de Fuca), Kelowna-West Kelowna, Nanaimo-Lantzville (excluding Protection
Island), Abbotsford, Chilliwack, and Mission. Most islands are excluded.