Modern software development reuses third-party libraries to cut costs but may introduce vulnerabilities. A critical practice is to verify the security of third-party libraries against public vulnerability reports. Many automated methods have been proposed to identify vulnerable libraries from vulnerability reports. Existing methods are designed for the generic identification of vulnerable libraries, considering the security of all software libraries. Generic identification is inherently challenging, resulting in limited accuracy. However, organizations only consider the security of libraries they trust and use, by self-managing a library whitelist. Therefore, we propose LibGuard, a framework to adapt existing methods to help organizations secure the libraries they use. LibGuard supplies a library whitelist for existing methods and filters the results according to a threshold, facilitating the discovery of risks overlooked by organizations while controlling false alarms. LibGuard is implemented in two ways. The first attaches the whitelist after existing methods. The second integrates the whitelist into existing methods. We evaluated LibGuard using 5,107 vulnerability reports and the library whitelist built from 79 Google projects and 29 Huawei projects. The results show that the two implementations of LibGuard increase the average F1 score by 10.25% and 11.77%, respectively. Moreover, LibGuard performs stably during the extension of whitelists. To our knowledge, this paper is the first study dedicated to securing self-managed third-party libraries, offering insights into adapting generic software security management to self-managed contexts.