You need to open a large channel. To do this, for example, you want to have over 2M sats on the on-chain wallet. Then you open a channel for 2M. The 2M on-chain becomes 2M Lightning plus the fees needed to complete the he on-chain transactions. Those sats are now permanently on Lightning until you close the channel. I wouldn't open a channel smaller than 2M. And you need several of them for the best experience. So, yes, your couple thousand is dust.