The Universe is transparent to gravitational waves at very early times (~ 10-45 s after the big bang) and a detection of gravitational waves from this time would be the most fundamental discovery that LISA could make. The CMB probes much later times (300,000 years after the big bang), although inflationary GW may leave a polarization imprint on the CMB
LISA will probe GW length and energy scales orders of magnitude shorter and more energetic than the scales probed by the CMB e.g. LISA will be able to probe the electroweak phase transition. However, LISA will not be sensitive enough to see a signature of GW emission from standard slow-roll inflation
Possibilities for relic gravitational wave emission