Most of them are upwards of $25 but here is a cheap half mortise lock:
https://www.ebay.com/itm/272763715013?hash=item3f81fbfdc5:g:CDQAAOSwb4Vbn~ho&amdata=enc%3AAQAIAAAAwOGp0LnosGWP3Ab9kmpbgttavIRwJ6RwORejT4cmxoqDmHUUy6X9SkzNHOomOJ9lVGWGIFUzv2AftQHBLE8rBs00nlIKi5S%2BEpH8%2BZqQ5lzQRETUFmunwhmwkrkHugZtBgMDpF3gRTeTMGFQ%2F5qCkJR8AQ1yNGK06wodEfxzpIFycsN4scKPKDx2I2cMExNBlcDvp2gooSuGQrets73LzCqa%2BEtDBFaI7ltQjuexW12bRJYYfefK%2Fo4XrPKniHNNMA%3D%3D%7Ctkp%3ABk9SR_CkuMO-Yg

Cheers, Jim ........................ Variety is the spice of life...............Learn something new every day