The speaker is a married woman who has had what some might call a difficult life. She had a 70 year marriage, and had 12 children, but 8 of them died before she was 60. She did a great deal of work, spinning, weaving, nursing the sick, and the man other activities all listed in the poem. Finally, at the age of 96, she "had lived enough, that is all" and "passed on to a sweet repose.
Given the disappointments and hard work of her life, you might expect some whinning --- but there is NONE. To her, this was life, and there was nothing to whine about. In fact, she is surprised to hear of "anger, discontent and drooping hopes" and can't imagine where they come from. She call the younger people "degenerate" and ends with the famous lines: "Life is too strong for you./It takes life to love life."
If I could directly answer your initial question, I'd say that her approach to life is take it as it comes, do what you have to do, don't expect that it owes you anything, enjoy all the little things that it has to offer, and you will "pass to a sweet repose." Sounds good to me ...
In "Lucinda Matlock," the speaker has a loving attitude toward life. She has loved and enjoyed every moment of her life and is grateful to have lived it in such a way. This attitude comes, perhaps, as a surprise to the reader since the speaker has clearly endured many hardships in her life. She has worked hard at keeping the house, for example, and has mourned the deaths of eight children. This has not dampened her enthusiasm for life, however: she fondly remembers raising her children and "rambling" over the hills while on holiday.
From the final lines of the poem, it is clear that the speaker wants to spread her message of love for life. She views people of this generation as angry and sorrowful and she challenges them to change this attitude by recognizing that life is difficult but can be conquered by accepting its many challenges:
Life is too strong for you —It takes life to love Life.