SIP was existing even before LTE technology. LTE technology just provides the fast path compare to other telecom access technologies to deliver services like ftp, browsing, IMS. In this way, SIP is an application level protocol. IMS is used to provide IP packets voice services.
Voice services can be provided through other mechanism such as CSFB. Operators who already have legacy network infrastructure they would go to use that legacy network to provide voice services and data services through LTE network in initial stage.