I've read this tutorial, but I haven't found there anything about reverse debugging. Does lldb have some features like target record in gdb? If yes, where can I read about it?
Not yet. To date most of the work on lldb has been to complete the common set of debugger features; it is solid for i386, x86_64, and armv7 debugging on Mac systems. There are people woking on Linux and *BSD ports now - that's hugely important to making lldb usable for lots of people. There are lots of interesting features that can be added to lldb in the future as the core debugger facilities are mature -- genuine reverse execution is one, process recording & playback (what I gather target record does) is another.