LTE is NOT backwards compatible with GSM, it is just the 4G technology agreed upon by virtually every GSM/HSPA carrier and the GSMA. LTE builds on HSPA, which is the 3G upgrade path. GSM uses a TDMA radio system while HSPA uses W-CDMA (not compatible with CDMA), and LTE uses E-UTRA, which is based on W-CDMA.
There was an LTE to CDMA handoff test here.
I think in the LTE RAN, there is a subsystem to allow legacy handoffs to all other technologies, potentially including WiMAX in the future.
I think initially, Verizon's LTE coverage will be limited to major cities only, and airports. Then they will slowly expand into the suburbs. But that expansion is going to take a while. I would imagine by 2013-2014, LTE would have the same coverage as 1X-EVDO has right now.