Perhaps start very small. I've yet to encounter lyrica on my travels, but legitely consume gaba 2700mg daily. It tends to have an impact on most other medications that I have taken (legitely) including tramadol, co-codamol (all three simultaneously as prescribed, 26 tabs a day in all) and later on, amytriptilene.
It depends how long anybody has taken gaba for, but perhaps they ought to reduce the dose if adding in lyrica.
As somebody else pointed out, hypothetically taking two seems somewhat redundant. Anybody consuming gaba ought to exercise caution if mixing with another class.