By default they do not, but it can be enabled, which is mentioned in the datasheet “The transmit PLL could also be routed via switches to the receive PLL so as to offer phase-coherent operation in TDD mode.”
And instructions how to enable TDD mode were provided for LimeSuite GUI and using the Lime Suite API.
But if TDD mode is not enabled, the default behaviour is to have a RX clock synthesizer and a TX clock synthesizer, which generate the shared RX local oscillator chain for both RX channels and a shared TX local oscillator chain for both TX channels respectively. LimeMicro:LMS7002M Datasheet - Myriad-RF Wiki