Do you think it's a better idea to move them to a lightning wallet like on electrum for example before the transaction fees get too high? I want to avoid paying a big amount just for one transaction in the main network
The fees are already too high. The best time to open a lightning channel is when fees are low because it requires an on-chain transaction. Lightning is meant for smaller payments so perhaps you shouldn't move your entire cold storage to lightning. I would just open a channel big enough for a few payments and occasionally top it off.
or recognize why it happens.
scrypt is the better algo for small sends.
both doge and ltc are dirt cheap to send coins . and they do it quickly.
they are not going away .
also so far no action against ordinals. so it appears the powers to be are fine with sending scrapes to ltc/doge for small payments.
no matter what btc does other than adding a viable coin for merge mining btc makes 1 block and ltc doge makes 12 blocks.