Synthetic brushes are fine for all of it .

What makes that paint a " lacquer " is the alcohol used in it .

That's the reason they dry faster .

" lacquers " technically use nitrocellulose resin but most of the hobby " lacquers " actually use acrylics .

You are fine with what you have  , but the water base acrylics  , like Vallejo , are easier to brush apply since they have more open time . They dry slower .

You can add retarder , propylene glycol , to those lacquer paints to give yourself more time and avoid leaving brush marks .