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bosh-init is the new name for the "bosh micro plugin". it's a cli tool that let's you install a single VM bosh release somewhere. the standard reason to use this is to deploy microbosh.
microbosh is a single VM installation of BOSH.
bosh-lite is a single VM installation of BOSH that creates containers in place of VMs on an iaas. it's typically used for development purposes because it's much faster to create and manage containers than VMs.
if your goal is to deploy lattice on openstack juno for development and evaluation use cases, then i would start by looking at the lattice Vagrantfile  and performing similar steps on an Ubuntu Trusty VM on Openstack.
if you want a production grade lattice environment with BOSH, then you'll need to deploy both cf-release and diego-release components co-located in a single deployment. this is an advanced bosh use case and i'd recommend starting with simpler BOSH scenarios first, like deploying redis with bosh .