This could potentially be linked to lyme disease, but I would err on the side of caution and assume that it's not.
The first thing we would want to rule out is a urinary tract infection. Your vet will likely recommend both a urinalysis and x-rays of the bladder to determine if there are any stones. A UTI and urinary stones can both cause the symptoms you're seeing.
If both of these are ruled out, a UTI and stones, your vet will likely talk to you about bladder contractility which can cause the walking and urinating, too. Sometimes its all the time, sometimes its not. But using a medication to help with contractility should work within a few days, if that's the concern. Your companion is getting up there in years, so this could be something that is linked to age.
Your vet will also want to be sure that the lyme disease has not caused some issues with the kidneys, so blood work may also be recommended.
For the time being, you can also look at a belly band for Mylo. These are tubes of fabric that are wrapped around the abdomen of male dogs and you use a feminine napkin on the inside of the fabric to absorb any urine that either leaks out (or, in the case of a marking dog, occurs from a hiked leg). This can help short-term but won't fix it long term. http://www.bellybands.net
Try to keep an eye on his water consumption because increased water intake and output may also indicate kidney disease, diabetes, Cushing's disease, etc.
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