$ git clone git://repo.or.cz/lyx.git lyx.git
$ cd lyx.git
$ git checkout --track -b follow-1.5 origin/BRANCH_1_5_X

$ git pull
$ ./autogen.sh && ./configure && make

This repository is made as follows. It was originally imported locally via a straightforward git-svn clone (this took 2 days):

$ git svn clone svn://svn.lyx.org/lyx/lyx-devel/  -T trunk -b branches -t tags

It is periodically updated locally and pushed to repo.or.cz as follows:

$ git svn fetch
$ git push -v ssh://gitmor@repo.or.cz/srv/git/lyx.git `git for-each-ref --format="%(refname)" 'refs/remotes/*' 'refs/remotes/*/*' | \
  perl -pe 's@^(refs/remotes/tags/)(.*)@$1$2:refs/tags/$2@ || s@^(refs/remotes/)(.*)@$1$2:refs/heads/$2@; s@/trunk$@/master@'`

(The inline Perl script translates the head and tag names from convention used by the Subversion repository to a more git-friendly convention.)