Inspect the lining of your tongue. These days most tongues are lined with a spongy foam material (exceptions apply). As the foam ages, it usually loses resiliency, and you end up tightening the laces to compensate. Overall result is the tongue digging in to your ankle or shin. Also, some foams become brittle as a result of age and exposure to sweat and skin oils. You end up with a crusty surface that digs in.
One option is to have a pro shop replace the foam. But this is typically pricey ($60+ in my area), and worth it only if there's plenty of life left in your boots otherwise (and assuming the boots were not el cheapo to begin with). Also, check around as to who does this properly. I had it done by a well-regarded pro shop in my area. They did do a good job; unfortunately, they used a low-grade foam (like packing foam) that fell apart after only 6 mos. Make sure they use a high-grade foam. Some manufacturers will also do it, but that means you'll be without boots for a while.
As suggested previously, an ankle gel sleeve can also help. A cheaper alternative to Bunga is Silipos (about half the price of Bunga). The Silipos works well, and is robust. However, it does not breathe, it collects sweat, and you should wash and dry it after every use [I believe that is also true of Bunga, but I have not personally used Bunga; someone else please chime in to confirm.].
If you don't want to use a gel sleeve, you can make a tongue liner pad to slip in between the tongue and the affected portion of your ankle or shin. I've have good success with thin Poron foam sheet, both sides lined with moleskin. I'd suggest you use the ultra soft (also called very soft) firmness foam. I'd start with 1/8" thick foam. Very compliant, robust, and low maintenance.
ETA: Not sure of your usage of "lace bite"; but not of consequence.