You cannot use LGPL code in a BSD-licensed project. When you are using LGPL'ed code the LGPL behaves very similar to the GPL. You can then only publish your project under the LGPL or GPL (even though some individual files in your project that do not depend on the LGPLed parts may use compatible licenses such as BSD).
A LGPL-licensed library can be used by a BSD-licensed project, as long as users (incl. all end users) are free to study and swap out the LGPLed parts of the software. This means either
- dynamically linking to the LGPL library, or
- distributing your project in a way that allows it to be relinked with a different version.
Note that the LGPL doesn't just bind you but also other people distributing your project. This would go beyond the usual requirements of the BSD license, so it is worth documenting these additional obligations in your project.
You do not have to link to the original LGPL code. In theory, you can slim down the LGPL'ed code to a smaller library that is still under the LGPL, but that you can link to in your project.