From the lfs doc: The exec env -i.../bin/bash command in the  .bash_profile   replaces  the running shell with a new one with a completely   empty  environment, except for the  HOME,  TERM, and  PS1   variables. This  ensures that no unwanted and potentially   hazardous environment  variables from the host system leak   into the build environment. The  technique used here achieves the  goal of ensuring a clean  environment.What case will cause that problem?Is there any simple example? 
Why lfs couldn't use original host environment variables?
environment variables;lfs
There are plenty of variables which will change how the shell behaves, what programs are executed or can hook into new programs. Examples for some of the more problematic environment variables are CDPATH, LD_LIBRARY_PATH, LD_PRELOAD, PATH. By resetting the environment you can ensure a clean and sane build environment without the need to take care/reset all kind of environment variables.