How long can my lightning node be safely offline?
that depends on the locktime that is configured for your channels. taken from c lightning (c.f.: https://github.com/ElementsProject/lightning/blob/97118c558e84e0b3a12a8cbe60528ad5cfcb2fd6/doc/lightningd-config.5.txt )


  watchtime-blocks='BLOCKS'::
      How long we need to spot an outdated close attempt: on opening a channel
      we tell our peer that this is how long they'll have to wait if they perform
      a unilateral close.
  
  max-locktime-blocks='BLOCKS'::
      The longest our funds can be delayed (ie. the longest watchtime-blocks
      our peer can ask for, and also the longest HTLC timeout we will accept).
      If our peer asks for longer, we'll refuse to create a channel, and if an
      HTLC asks for longer, we'll refuse it.


I believe the standard setting should be 144 blocks which statistically should be 24 hours. of course you should consider a safety window to be able to get your breach remedy tx mined in case of a unilateral close.