What about menthol lozenges for coughing and sore throats?

I think they are an excellent idea. Caveat: there is no published studies I am aware of that support this. From here on, the details get more complicated. I just spent 45 minutes reading the list of ingredients and checking prices at Publix.

1. There are many brands (Cepacol, Chloraseptic, Fisherman's Friend, Halls, Lundgrens, generic Publix, Ricola, Sucrets) and variations of ingredients. They all fill up an entire small section at the pharmacy. The common ingredient in almost of all of the lozenges is menthol. Note, the amount of menthol varies from about 3g up to 10 g.
2. Some products say mentho-lyptus, the latter half meaning eucalyptus. Some times this is listed as an inactive ingredient and a few times it is listed as an active ingredient. I do not think eucalyptus adds much to the results.
3. Other active ingredients include: pectin (demulcent: forms a film over a mucous membrane, for soothing and protection); dyclonine (an oral anesthetic); benzocaine (an oral anesthetic); dextromethorphan (cough suppressant). The herbs listed on the label of Ricola products are listed under the inactive ingredients, which seems like false advertising to me.
4. Other variables include: the number of lozenges per bag, prices per lozenge (3.3 to 10 cents), number of calories per lozenge (since sugar is usually used), flavors, sugar or sugar-free (diabetics beware).
5. Beware of other products being sold as mints, such as Altoids. They taste great (I have a sweet tooth), however looking at the ingredients, I suspect I'm getting more sugar than medicine. So I would not recommend these for cough suppression.

I find menthol to be soothing for my throat, reduces some coughs, and a decongestant for my nose, so I use them when I have a cold (which is now.) My choice is whichever product gives the most menthol for the least price and least number of calories. If you have questions about using lozenges for cough relief, ask your doctor...