I am somewhat confused about when to apply grub control on a lawn,
The best time to apply grub control is in July…”apply in July when the beetles fly”. Here’s a link that explains grub control.
Moles are active now
Treating for grubs may discourage moles but moles also eat earthworms so, using grubs control doesn’t automatically mean your moles will move on…they won’t. The way to rid you lawn of moles is to use a mole repellent like MoleMax. Here’s a link that describes methods of mole control.
and it was my understand to apply lime in the fall to kill grubs.
Sorry, lime doesn’t kill grubs (or anything at all) but is used to correct soil acidity. A pH test should be done before applying lime. Here’s a link to all you need to know about soil pH testing and lime applications
What product should be applied now (spring) for control of moles and other insects that want to eat my lawn?
The only insects to possibly be concerned about are ticks and ants. These aren’t a problem for your lawn but, if you want to treat for them there’s this.