I think it is the fear of losing money to a bug. I don't follow LN closely but I hear the LN devs warn people about possibility of bugs and how they shouldn't use it with large amounts. It is understandable that an exchange doesn't want to bother with the technology until it is matured.
There is a great article on the topic of LN vulnerabilities. I don't know if you have read it, but if you are interested, here is the link >
https://www.coindesk.com/bitcoin-lightning-network-vulnerabilities-not-exploited-yet.
One of the most severe threats is called a Time-dilation eclipse. The article mentions that light clients, such as Blue Wallet or Phoenix Wallet are particularly vulnerable to this attack vector. To carry out such an attack the scammer would have to create a whole network of nodes that the victim would be connected to. The victim is then only connected to malicious nodes. The scammer can deliberately slow down the process of sharing transaction data with his victim. He can close the channel and steal the coins before this data is received by the victim. That's the idea anyway.
I only know one exchange (Bitfinex) that has an LN channel and they started it with a very small capacity for this very risk, then increased it after some time passed but it is still a small capacity.
If
this article can be trusted, and it seems to be up-to-date, the list of exchanges that accept LN payments is slowly on the rise. Besides Bitfinex, there is OKCoin and OKEx. Paxful has declared intention to integrate the LN...etc.