Since Henry has 30 more lollipops than Alison, he has 60+30= 90 lollipops.
Together, Alison and Henry have 90+60 = <<90+60=150>>150 lollipops.
Alison has half the number of lollipops that Diane has, meaning Diane has 2*60 = 120 lollipops.
Altogether, the three have 120+150 = <<120+150=270>>270 lollipops.
Since they eat 45 lollipops each day, they'll take 270/45=<<270/45=6>>6 days to finish all the lollipops.
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