For 'dichten', Siehe Wörterbuch: dichten . . .

for 'trachten', check:

to aspire = trachten |trachtete, getrachtet|
to strive after = nach etw. trachten |trachtete, getrachtet|
to strive for nach etw. trachten |trachtete, getrachtet|
to endeavorAE, endeavourBE to = trachten zu |trachtete, getrachtet|
to aspire to do sth. = danach trachten, etw. zu tun
to seek to do sth. = danach trachten, etw. zu tun [form.]
. . .

Thanks, but I thought there might be some special use here. When they are together in this context, how can they become lazy if they have aspirations?

Actually, you are right. It doesn't make sense.
"Dichten und trachten" in a religious or old-fashioned poetic context does mean "planning, striving", that is correct. It does not really go together with being lazy.
Maybe you can give us a bit more context?

Could that be it (not a very literal translation of course)?

"Dichten" in this context does NOT mean "to write poetry" or any of the other usual translations. In the old-fashioned poetic context of "trachten" it is used synonimously.

Ist ein bisschen alt.
s. Grimm 4. nach etwas, auf etwas dichten, trachten etwas zu erreichen. (Dort letztes Beispiel von Schiller, 1759-1805)