While looking to do this I ended up on this thread, in the spirit of more information for the next person...
In the the latest web app builder at the time of this post I added to my config.json the code below which gets dealt with within the api "somewhere". lods is in MapOptions at the same level as the extent.
"mapOptions": {
"extent": {
"xmin": -1,
"ymin": -1,
"xmax": -1,
"ymax": 1,
"spatialReference": {
"wkid": 102100
}
},
"lods" : [
{ "level" : 0, "resolution" : 156543.033928, "scale" : 591657527.591555 },
{ "level" : 1, "resolution" : 78271.5169639999, "scale" : 295828763.795777 },
{ "level" : 2, "resolution" : 39135.7584820001, "scale" : 147914381.897889 },
{ "level" : 3, "resolution" : 19567.8792409999, "scale" : 73957190.948944 },
{ "level" : 4, "resolution" : 9783.93962049996, "scale" : 36978595.474472 },
{ "level" : 5, "resolution" : 4891.96981024998, "scale" : 18489297.737236 },
{ "level" : 6, "resolution" : 2445.98490512499, "scale" : 9244648.868618 },
{ "level" : 7, "resolution" : 1222.99245256249, "scale" : 4622324.434309 },
{ "level" : 8, "resolution" : 611.49622628138, "scale" : 2311162.217155 },
{ "level" : 9, "resolution" : 305.748113140558, "scale" : 1155581.108577 },
{ "level" : 10, "resolution" : 152.874056570411, "scale" : 577790.554289 },
{ "level" : 11, "resolution" : 76.4370282850732, "scale" : 288895.277144 },
{ "level" : 12, "resolution" : 38.2185141425366, "scale" : 144447.638572 },
{ "level" : 13, "resolution" : 19.1092570712683, "scale" : 72223.819286 },
{ "level" : 14, "resolution" : 9.55462853563415, "scale" : 36111.909643 },
{ "level" : 15, "resolution" : 4.77731426794937, "scale" : 18055.954822 },
{ "level" : 16, "resolution" : 2.38865713397468, "scale" : 9027.977411 },
{ "level" : 17, "resolution" : 1.19432856685505, "scale" : 4513.988705 },
{ "level" : 18, "resolution" : 0.597164283559817, "scale" : 2256.994353 },
{ "level" : 19, "resolution" : 0.298582141647617, "scale" : 1128.497176 },
{ "level" : 20, "resolution": 0.14929107082380833, "scale": 564.248588 },
{ "level" : 21, "resolution": 0.074645535411904245, "scale": 282.124294 },
{ "level" : 22, "resolution": 0.0373227677059521225, "scale": 141.062147 }
]
},