Although L'Engle was capable of painting in a traditional representational manner (see the portraits below), he became a run-of-the-mill, middle-of-the-road modernist of the 1920-1940 variety that I describe in the book Art Adrift. Not that his paintings were bad; he was a competent artist. But they were typical of his times, where many painters had to decide whether or not to accept modernism, and if they did, to what extent they would embrace it.
Like many of his contemporaries, L'Engle never quite settled on a distinctive, personal style. Instead, he drifted along, following the American modernist fashions of his day.
Update - 8 February 2015 -- The images on the original post were removed at the request of their copyright holder who also requested that I remove the link to the official L'Engle web site, to which I complied. I retained the image captions so that interested readers can track them down using Google image search.
Self-Portrait - 1914
The "L'E" symbol on many of the images here is probably related to a source claiming copyright, which I hereby acknowledge, if that is so.
Portrait of Lucy - 1919
Lucy was his wife, and also an artist.
Cranberry Pickers - 1926
Trapeze Artists - 1926
Martha Graham Dancer - 1927
Madeline and Thelma - 1930
Paintings on front and back of panel.
Building New York - 1935
Cuban Scene - 1938
Nightmare, or the End - 1954
Sacrifice of Abraham - 1957
Painted the year of his death.