Is it possible to use LGPL as a library in a commercial product without opening the product code

As I understand it, the LGPL with the linking must be dynamic (so the user could, if desired, to replace the library), the license must be included, and will need to specify where the source code of the library either include a written commitment to provide them on request.
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With the GPL, all code should be under GPL and the code to open need to (or as above to give a pledge). Usually pay attention to what code you are obliged to open only to those with whom you are bound by the terms of the license, that is to whom you deliver the finished product.

Linking is necessarily dynamic. In fact, the publication shall be subject to the code of those modules which are written using LGPL code. Static linking embeds the code directly in the module, therefore, also falls into this category.
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GPL can be used in closed projects, if the relationship between the components takes place not by loading into the address space of the process and, for example, run the GPL-program as a separate process and communicate with it via pipes. There is only another subtle point regarding the proliferation of such combination product: GPL-program cannot be combined in one package with the proprietary unless it is aggregate (a set of separate, interrelated software packages with which users can work independently; for example, selection for publication on CD). But the difference between two separate programs and one program consisting of two parts, often too subtle and uncertain.
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I recommend reading the GPL FAQ.

So, to summarize. In order not to open their codes we:
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1) Use the LGPL for dynamic linking
2) Use a separate app on any (?) licenses and interact with them as an external app
3) you can use GPL in closed projects, if the relationship between the components takes place not by loading into the address space of the process and, for example, run the GPL-program as a separate process and communicate with it via pipes.
4) Use the BSD license
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if wrong please correct, thanks!