LEDE uses Dnsmasq and there has been a request on the Dnsmasq mailing list last week to implement DNS-over-TLS to it: http://lists.thekelleys.org.uk/pipermail/dnsmasq-discuss/2017q4/011804.html
I don't know if there are any other possibilities besides waiting on an implmentation in Dnsmasq.
Unbound supports DNS-over-TLS and is available as a package in LEDE. So, you can install Unbound and use it as a DNS resolver instead of Dnsmasq. You can/should still use Dnsmasq as a DHCP server, though, and maybe forward local domain lookups to it as well. Just look for a tutorial how to set up Unbound on LEDE or OpenWrt.