Swap tokens directly on DEX or sell on exchange and buy ETH to swap?

I'm pretty new to the DEX thing so forgive me if this is a rookie question. I've got a stack of LRC that I'm finally thinking of ditching. It's currently on a cold wallet. If I want to swap it for an ERC-20 token on a DEX (have been using 1inch so far), is there any reason to send it back to the exchange and sell, then buy ETH and send to wallet for swap? Or will it be cheaper just to swap directly for the LRC? I guess what I'm asking, is firstly, can you swap any token for any token (network permitting) and secondly, are the fees and exchange rates pretty much the same?, or would I somehow lose out by swapping directly? Say if there's not as much liquidity for LRC than there is with ETH, would I pay more for that swap somehow? Thanks