Having had several horses and two dogs who have had fairly serious cases of Lyme has made me a strong advocate of testing for Lyme when the slightest suspicion arises, such as a change in disposition, the favoring of one leg, or a bit of unexplained stiffness. There are at least two options in terms of tests for Lyme (and sometimes other tick-borne diseases). One is a quick, on the spot test done by your veterinarian, with the results available in about 15 minutes. The other test is the Cornell Lab test which must be sent in, and therefor takes longer & is typically more expensive, but it provides much more specific information.
Your veterinarian can guide you with regard to which test she/he recommends. A call to your clinic can also provide you with an idea of how many cases of Lyme have occurred in your area or in general whether or not there is a high incidence of the disease. Thankfully Lyme is treatable with the antibiotice Doxycycline, and it is not uncommon for your horse to make a full recovery, if the disease is caught early and treated completely. Unfortunately, Lyme can recur...so it's important to remain vigilant.
It is so important to catch this early, as you say! The tick season is upon us, especially with the wet conditions!