The long-term mooring option definitely isn't ideal for a TI, but it can easily be done on a lake (and I completely understand the convenience factor)!
I have only dropped anchor for swimming/diving and an occasional overnight (all while I was present/nearby), but haven't experience any issues even in heavy winds and moderate swells, so I would think the main concerns besides prolonged sun exposure in your lake situation would be growth of algae, etc. on the hull and the possibility of theft.
You can make a basic anchor yoke (to attach from the akas/ near the connection point to the center hull), and you might potentially consider folding-in the amas/outriggers at anchor and securing the sail atop the main hull inside a storage bag, then covering everything with a waterproof UV-protective cover as well.
As far as the mooring itself, again, I've only attempted temporary anchorages with my TI (I use the same Fortress FX-11 anchor for all of my boats), but have also used an assortment of anchors (ranging from lightweight mushroom and helix style to 8k lb blocks of granite) with success for seasonal mooring of a center-console in coastal/tidal regions, but you shouldn't require nearly that much holding power for a knee-to-waist-deep lakebed.
I started to type up a summary of calculating chain/line scope VS depth and other mooring factors but came across this page with pictures that will probably be more helpful when it comes to semi-permanent moorings:
https://support.jamestowndistributors.c ... nt-mooring...Hopefully someone else chimes in who has had some success with long-term mooring of a TI!