HTC Desire had some nasty bugs, try updating firmware on the device or clearing cache from the recovery menu that android phones have, Also try this fix i found on forums regarding HTC Desire 520 and the lag issues it experiences.
HTC Desire HD - Laggy and Slow - Issue identified and fixed
If you find your HTC Desire running slow, laggy, or a bit sluggish, then it's most likely related to the /init issue as identified on the XDA forums. The /init process kicks in and consumes around 80-90% of the CPU constantly making it laggy to swipe, gallery very slow and jerky for most actions. This is easy to identify by running a process manager like Watchtower which will reveal this. Restarting the phone resolves this for a few hours or maybe even a day.
However, the XDA forums have found a workaround.
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"A fix has been found to stop the /Init process lagging the phone.
On your phone go to..
Menu/settings/applications/development/now turn on Usb debugging..
This seems to keep the / init process at 0% CPU usage, it also works when the /INIT problem starts, turning USB debugging on will make the /INIT process drop back to 0%, very nice to see."
===QUOTE===
I'm testing this today, but am pretty confident as most users were testing it over the weekend. I experience the lag after only a few hours from a device restart. The downside is that it causes your PC to try and find a driver when you connect it up as a USB device. However, not installing one will not prevent you from using it.