Mixture of mistaken memories as well as wanting to hide his double life. Made him look guilty when he actually wasn't, at least not of what he had been accused of in this instance.

He was private about some parts and right out remembered some parts wrong.
Fact is we do a lot of things on auto-pilot without thinking to much about them and we dont store all the informations individually. If someone asked me what I ate 5 days ago Id have problems remembering (unless it was som sort of special event). As someone who is out there running a lot myself I for one like to diversify my route because its lae arse boring to run the same route every day. If however you ask me wich one I was running a specific day sone time back I wouldnt be able to tell you (well aside from the fact that I could find out since I use a running app).
If you add variables like a dog that sometimes joins and throw in a interrogator who is out to get me to setle some score you can see how easy it is to get confused and end up looking like a complete liar.

He lied in the beginning because he felt superior, and thought it was ridiculous that he could be a suspect. So he was just throwing random answers at them. He then continued to lie because he didn't want his private affairs aired.
The photos were obviously a coincidence.
"Life's tough. It's even tougher if you're stupid." John Wayne

"The real issue was why did they set him up to do a totally stupid and unrealistic thing, namely find the body, go home undress, call police, shower and wait for them to arrive."
We don't really know how much of that is true, because that part you refer to, was part of the wife's testimony and by the end of the film we are questioning just about every thing she did and said.
The OP's question is a good one and I'm not sure even now why he appeared to create so much trouble for himself.
May be he was just forgetful, may be he wasn't thinking straight or may be he was just becoming totally depressed with his wife's behaviour and it adversely affected his judgement.

The real issue was why did they set him up to do a totally stupid and unrealistic thing, namely find the body, go home undress, call police, shower and wait for them to arrive. Why not do what anyone else would do, run out of the bushes and call for help . . . Yes, I know it is a movie and stupid things happen in movies, but they set it up in such a way that it all falls apart when you look at the first string. The one that makes the cops suspicious is the least likely of all the things to happen. That he would lie about everything else makes sense, that he would act like that when encountering a corpse, NO.

Sure but not about that. He did actually find the girl after somebody else killed her.

I don't know what movie you were watching but he lied about a NUMBER of things throughout the interrogation.

He did not lie he did find the girl !
by chance, indeed.

Perhaps the Photo album the cops found later is the main reason why he lied to Freeman. Because it made him suspicious.
further, he obviously didnt want the conflict with his wife revealed, so he gave more lies.

He ran with the dog so much that he thought the dog was with him when he found the girl but later remembered that he wasn't.
Photography was a hobby of his so I'm sure he took lots of pics of everything in his town