From what I can tell, while the free visa exemption is not available for a Lithuanian passport holder, you do qualify to get a 15-day visa on arrival at 24 designated border crossings. It looks like you'd need to have proof of onward travel out of Thailand within 15 days, 2 passport-sized photos, and the 1,000 Thai baht fee. Unfortunately, it does not look like the border crossing at Chong Mek is one of the 24 international crossings where this is possible.
Full details are at this link: http://www.mfa.go.th/web/2482.php?id=2491
As an alternative, you could always apply for a multi-entry tourist visa ahead of time. That might solve a few logistics problems for you as well as purchase some peace of mind. Good luck.