Q1: If somebody starts the dream with lucid mode you will run out of cards in the first round, after this you need to remember and that is your only option?
Q2: If you have enough ether you can go to lucid mode getting all your cards?
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Perhaps you set up the lucid mode incorrectly? You simply take all lucid mode cards and shuffle them to then put them on top of your regular influence deck (the deck you draw from normally). You need to discard your hand before drawing your hand limit of lucid mode cards (typically 6). And after using those, they go to a separate special pile (not the regular sealed cards pile, nor the standard discard pile). You are also not allowed to reshuffle your influence deck with lucid mode cards on top. This basically ensures you need to first use all your lucid cards before going back to the regular mode (by having all used lucid cards in the special used pile).
This means all unseal mechanics only work with the non-lucid cards. I wish they picked a different name for the lucid discard pile rather than calling those cards "sealed" as this is misleading a bit.
What I wonder is, what happens if you need to seal the top card from your deck and it is a lucid card. My guess is, it is discarded, otherwise it would break the mechanics.
Q1: Yes, you cannot reclaim Lucid cards in any other way, as they have their own pile of Sealed Lucid cards. When you Remind in this Dream, you unseal "normal" cards. But, you may reclaim Lucid cards by entering the Lucid Mode again.
Q2: As above - you may always pay Ether to enter the Lucid Mode again.