Yes, it is much more than just keeping track of a private key.
One has to be able to use one’s guesses to put a channel that hits on-chain (or to burn the depot if there are multiple hits). This requires the depot parameters, etc. along with the guess information (including the list of random factors F_i).
One also needs the latest Lightning channel state for each active Lightning channel.
Note: Apologies in advance for what are likely to be slow responses.