Peter, what is your buffer set to? I suggest you set it to the maximum (largest) buffer size. If you do any live recording with Logic, investigate and learn how to do live monitoring from your interface instead of Logic to deal with the large buffer setting during live takes. This is the way I work all the time. All my Logic settings/buffers are as large as possible so I can get ridiculous amounts of DSP in my laptop. People usually run from this and seek the shortest audio buffer size, because configuration an audio interface (that can do live input monitoring) is a learning curve in an of itself. But you can wait on that for now and just test out your system with the large buffer to see if it helps.
I use an RME Fireface 400, which gives me the ability to monitor vocals and instruments live. In the audio driver window, I have monitoring unchecked. This means I can not monitor audio input through FX inserts in Logic, but I don't care. Once they are recorded, I can play the tracks back normally with FX. I have outboard distortion and reverb devices just so I can monitor with some rudimentary FX via the interface, knowing as soon as the dry tracks are recorded in Logic, I can get the exact mix I am looking for. Obviously, I'm not explaining the routing on the Fireface 400 in this response; it's a time-consuming subject. But try the large buffer setting at least (in the audio driver window) and see if it helps.