Synonyms for Lay out:

n.

collate, layer, pile, sort, heap. fund, invest, finance, invest in, pay out, bear the cost/expense etc., spend, lend. display, illustrate, run-through, put across, explain, clarify. architecture, civil engineering, architectural, landscape architecture, engineering, feng shui, ground plan, elevation. casket, coffin, box, cremains, cremate, bury, bier, burial, Ashes, cortege. burn, sunbathe, sun, sun cream, sunburn, overexpose, bask, SPF, sunburned. fell, knock, floor, punch someone's lights out, knock-down, flatten, deck, take down, strike down. expenditure (noun)
installment, outlay, payment, disbursement, purchase, investment, expenditure.
lay out (noun)
range, set, set out, array, set up, represent, present.

v.

change (verb)
set up, set.
design, plan (verb)
set out, display.
spend money (verb)
invest, lend, outlay.

Other synonyms:

clarify, engineering, ground plan, invest, feng shui, heap, architectural, SPF, collate, sun cream, explain, civil engineering, put across, spend, landscape architecture, bury, sunbathe, sunburned. illustrate, overexpose, sun, run-through, layer. architecture, pile, sort, strike down, fell. knock-down, elevation. deck, flatten, take down. floor. knock. burn. blow
pay out.