As a homebrew creator, GM, and player, Lancer without ranges or otherwise grid-based combat is nigh-impossible to execute. You would have to have, at minimum, categories for Engaged, Point Blank (Range 2, for House Guard and White Witch), Close Range (3, for Monarch's Avenger Silos and similar), Short Range (5), Medium Range (10), Long Range (15), and Extreme Range (20). That's without accounting for Speed, Cone weapons, Blasts above Blast 2 (Blast 1 and 2 can be represented hackily with this measure), any intermediate weapons ranges (such as Range 8, which comes up a surprising amount), et cetera.
While I am sympathetic to the cause of accessibility, I've played a whole lot of 40k - as you have as well. 40k has a basic accessibility floor as embodied in needing at minimum terrain, miniatures that can accurately represent True Line of Sight, and a table large enough to provide meaningful room to tactically engage (all things Lancer also requires) - but 40k fans over the decades have made immense strides in accessibility on these fronts by simple ingenuity. "Poorhammer" terrain, whether it's prettying up shoeboxes or printing out paper stock; printing out images of or drawing units and tacking them upright to avoid miniatures; playing on the floor when you just don't have a table big enough. I should know, because that's how I had to play for awhile.
In a similar way, there are minimal considerations for Lancer as a system to function that can't be removed - an accessibility floor. One of those, to at least some extent, is gridded combat. I know Tom's been musing on Lancer 2e being far closer to ICON than 1e, and at that point these considerations may change - as others have brought up in reference to how ICON handles its combat.