Your stated pressure doesn't make sense.
lb, that's pounds per square inch, (PSI) OR bar. not both. 35 PSI is a bit low for that size tire, I would recheck what the sidewall says, and make sure you have the recommended minimum.
That pump should be good for pumping the tires at home, but would be a bit big for taking on the ride.
Lezyne makes some nice take along pumps, but not cheap.